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In this paper, we introduce the notion of curved O -operator systems as a generalization of T. Brzeziński's (curved) Rota-Baxter systems, and then investigate their relations with O -operator systems, (tri)dendriform systems, pre-Lie algebras, associative Yang-Baxter pairs and quasitriangular covariant bialgebras. [ABSTRACT FROM AUTHOR]

In this paper, all super-skewsymmetric super-biderivations of twisted N = 1 Schrödinger-Neveu-Schwarz algebra are determined. It is shown that all the super-biderivations are inner. Furthermore, the linear super-commuting maps of twisted N = 1 Schrödinger-Neveu-Schwarz algebra are standard. [ABSTRACT FROM AUTHOR]

This paper is dedicated to studying for the first time the concept of two-fold differential equations of different orders and different types, where we present the solutions for twofold fuzzy differential equations, and for two-fold neutrosophic differential equations. Also, we illustrate many numerical examples to clarify and explain the novelty of this work. [ABSTRACT FROM AUTHOR]

Suppose that S T 1 is a class of close-to-star functions. In this paper, we investigated the estimate of Zalcman functional on the logarithmic coefficients and the third Hankel determinant for the class S T 1 with the determinant entry of logarithmic coefficients. Also, we obtained the sharp bounds of Zalcman functional J 2 , 4 f and J 3 , 3 f for the class S T 1 . [ABSTRACT FROM AUTHOR]

The present paper is devoted to the study of 2-local derivations on the Schrödinger-Virasoro Algebra, which is an infinite-dimensional Lie algebra with three outer derivations. We prove that all 2-local derivations on the Schrödinger-Virasoro Algebra are derivations. [ABSTRACT FROM AUTHOR]

In this paper, we give a complete classification of all free $ U(\mathbb {C}L_0 \oplus \mathbb {C}Y_0\oplus \mathbb {C}M_0) $ U (C L 0 ⊕ C Y 0 ⊕ C M 0) -modules of rank 1 over a Schrödinger-Virasoro type algebra $ \mathfrak {tsv} $ tsv . [ABSTRACT FROM AUTHOR]

In this paper, we prove a result similar to results of Itoh [J. Algebra 150 (1992), pp. 101–117] and Hong-Ulrich [J. Lond. Math. Soc. (2) 90 (2014), pp. 861–878], proving that integral closure of an ideal is compatible with specialization by a general element of that ideal for ideals of height at least two in a large class of rings. Moreover, we show integral closure of sufficiently large powers of the ideal is compatible with specialization by a general element of the original ideal. In a polynomial ring over an infinite field, we give a class of squarefree monomial ideals for which the integral closure is compatible with specialization by a general linear form. [ABSTRACT FROM AUTHOR]

In this paper we show how the Functional Separation of Variables (FSoV) method can be applied to the problem of computing overlaps with integrable boundary states in integrable systems. We demonstrate our general method on the example of a particular boundary state, a singlet of the symmetry group, in an su 3 rational spin chain in an alternating fundamental-anti-fundamental representation. The FSoV formalism allows us to compute in determinant form not only the overlaps of the boundary state with the eigenstates of the transfer matrix, but in fact with any factorisable state. This includes off-shell Bethe states, whose overlaps with the boundary state have been out of reach with other methods. Furthermore, we also found determinant representations for insertions of so-called Principal Operators (forming a complete algebra of all observables) between the boundary and the factorisable state as well as certain types of multiple insertions of Principal Operators. Concise formulas for the matrix elements of the boundary state in the SoV basis and su N generalisations are presented. Finally, we managed to construct a complete basis of integrable boundary states by repeated action of conserved charges on the singlet state. As a result, we are also able to compute the overlaps of all of these states with integral of motion eigenstates. [ABSTRACT FROM AUTHOR]

This paper addresses the recent body of research in algebra and algebraic thinking from 2018 to 2022. We reviewed 74 journal articles and identified four clusters of content areas: (a) literal symbols and symbolizing, (b) equivalence and the equal sign, (c) equations and systems, and (d) functions and graphing. We present the research on each of these content clusters, and we discuss insights on effective teaching practices and the social processes supporting algebraic reasoning. The research base shows that incorporating algebraic thinking into the elementary grades, emphasizing analytic and structural thinking processes, and emphasizing covariational reasoning supports students' meaningful learning of core algebraic ideas. We close with a discussion of the major theoretical contributions emerging from the past five years, offering suggestions for future research. [ABSTRACT FROM AUTHOR]

In this paper, we exploit necessary/sufficient optimality conditions for ε-quasi positively properly efficient solutions of the semi-infinite multiobjective optimization problems with data uncertainty. We also consider Wolfe type dual problems/Mond--Weir type dual problems under the assumptions of generalized convexity. Finally, several illustrative examples are also provided. [ABSTRACT FROM AUTHOR]

This paper concerns with convergence properties of an inertial proximal algorithm that contains a Tikhonov term regularization, time scale parameter, and a Hessian-driven damping in a Hilbert space. More precisely, we prove the strong convergence of the proximal algorithm obtained by temporal discretization of a continuous dynamic that we treated earlier in a previous work. We also obtain the convergence of the values to the global minimum of the objective function, and a strong convergence of the gradient and the velocity towards zero. Finally, we present a numerical example to illustrate our results. [ABSTRACT FROM AUTHOR]

To elucidate the combinatorial architecture of neural codes, the neural ideal , an algebraic object, was introduced. Represented in its canonical form, provides a succinct characterization of the inherent receptive field architecture within the code. The polynomials in are also instrumental in determining the relationships among the neurons' receptive fields. Consequently, the computation of the collection of canonical forms is pivotal. In this paper, based on the study of relations between pseudo-monomials, the authors present a computationally efficient iterative algorithm for the canonical forms of the neural ideal. Additionally, we introduce a new relationship among the neurons' receptive fields, which can be characterized by if-and-only-if statements, relating both to and to a larger ideal of a code . [ABSTRACT FROM AUTHOR]

We describe some recent computer investigations with the 'Constraint Logic Programming over Finite Domains' library in the Prolog programming environment to search for new simple Lie algebras over the field \operatorname {GF}(2) of 2 elements. Motivated by a paper of Grishkov et al., we specifically look for those with a thin decomposition , and we settle one of their conjectures. We extrapolate from our results the existence of two new infinite families of simple Lie algebras, in addition to finding seven new sporadic examples in dimension 31. We also better contextualise some previously discovered simple algebras, putting them into families which do not seem to have ever appeared in the literature, and give an updated table of those currently known. [ABSTRACT FROM AUTHOR]

Let K be a field of characteristic zero and x a free variable. A K - ℰ -derivation of K [ x ] is a K -linear map of the form I , − , ϕ for some K -algebra endomorphism ϕ of K [ x ] , where I denotes the identity map of K [ x ]. In this paper, we study the image of an ideal of K [ x ] under some K -derivations and K - ℰ -derivations of K [ x ]. We show that the LFED conjecture proposed in [W. Zhao, Some open problems on locally finite or locally nilpotent derivations and ℰ -derivations, Commun. Contem. Math. 20(4) (2018) 1750056] holds for all K - ℰ -derivations and all locally finite K -derivations of K [ x ]. We also show that the LNED conjecture proposed in [W. Zhao, Some open problems on locally finite or locally nilpotent derivations and ℰ -derivations, Commun. Contem. Math. 20(4) (2018) 1750056] holds for all locally nilpotent K -derivations of K [ x ] , and also for all locally nilpotent K - ℰ -derivations of K [ x ] and the ideals u K [ x ] such that either u = 0 , or deg u ≤ 1 , or u has at least one repeated root in the algebraic closure of K. As a bi-product, the homogeneous Mathieu subspaces (Mathieu–Zhao spaces) of the univariate polynomial algebra over an arbitrary field have also been classified. [ABSTRACT FROM AUTHOR]

For an ample groupoid and a unit x of , Steinberg constructed the induction and restriction functors between the category of modules over the Steinberg algebra A R () and the category of modules over the isotropy group algebra R x . In this paper, we prove a graded version of these functors and give a description of spectral graded simple modules over the graded Steinberg algebra A R (). As an application, the spectral simple and graded simple modules over the Leavitt path algebra L K (E) are classified. In particular, we show that many of previously known simple and graded simple L K (E) -modules, including the Chen simple modules, are induced from (ungraded or graded) simple modules over isotropy group algebras. [ABSTRACT FROM AUTHOR]

Given a Hopf algebra H , Brzeziński and Militaru have shown that each braided commutative Yetter–Drinfeld H -module algebra A gives rise to an associative A -bialgebroid structure on the smash product algebra A ♯ H. They also exhibited an antipode map making A ♯ H the total algebra of a Lu's Hopf algebroid over A. However, the published proof that the antipode is an antihomomorphism covers only a special case. In this paper, a complete proof of the antihomomorphism property is exhibited. Moreover, a new generalized version of the construction is provided. Its input is a compatible pair A and A op of braided commutative Yetter–Drinfeld H -module algebras, and output is a symmetric Hopf algebroid A ♯ H ≅ H ♯ A op over  A. This construction does not require that the antipode of H is invertible. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study a poset isomorphism between two support \tau-tilting posets. We take several information from combinatorial properties of support \tau-tilting posets and give an analogue of Happel-Unger's reconstruction theorem. [ABSTRACT FROM AUTHOR]

Building on work of Ruelle and Putnam in the Smale space case, Thomsen defined the homoclinic and heteroclinic C^\ast-algebras for an expansive dynamical system. In this paper we define a class of expansive dynamical systems, called synchronizing dynamical systems, that exhibit hyperbolic behavior almost everywhere. Synchronizing dynamical systems generalize Smale spaces (and even finitely presented systems). Yet they still have desirable dynamical properties such as having a dense set of periodic points. We study various C^\ast-algebras associated with a synchronizing dynamical system. Among other results, we show that the homoclinic algebra of a synchronizing system contains an ideal which behaves like the homoclinic algebra of a Smale space. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of v-stable silting-discrete algebras, which unify silting-discrete algebras and tilting-discrete self-injective algebras, where v is a triangle auto-equivalence of the bounded homotopy category of finitely generated projective modules. Moreover, we give an example of tilting-discrete self-injective algebras which are not silting-discrete. [ABSTRACT FROM AUTHOR]

In this paper, we give a necessary and sufficient condition for an almost Jordan algebra, which is also called Lie triple algebra to be an evolution algebra. We study the nilpotency, power associativity of such algebras. We specify the necessary and sufficient conditions for such an algebra to be baric. Along the way we show that train evolution algebras which are almost Jordan algebras are of rank at most 5. We prove that any finite-dimensional non-nil-evolution algebra verifying the identity of almost Jordan algebras has at least one non-zero idempotent. Finally, we study the derivations of this class of algebras. [ABSTRACT FROM AUTHOR]

Copyright of Cahiers de Topologie et Geometrie Differentielle Categoriques is the property of Andree C. EHRESMANN and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

It has been shown that by using a Lagrange multiplier field to ensure that the classical equations of motion are satisfied, radiative effects beyond one-loop order are eliminated. It has also been shown that through the contribution of some additional ghost fields, the effective action becomes form invariant under a redefinition of field variables, and furthermore, the usual one-loop results coincide with the quantum corrections obtained from this effective action. In this paper, we consider the consequences of a gauge invariance being present in the classical action. The resulting gauge transformations for the Lagrange multiplier field as well as for the additional ghost fields are found. These gauge transformations result in a set of Faddeev–Popov ghost fields arising in the effective action. If the gauge algebra is closed, we find the Becci–Rouet–Stora–Tyutin (BRST) transformations that leave the effective action invariant. [ABSTRACT FROM AUTHOR]

This research article introduces and investigates the concepts of quasi covered ideals and quasi bases within the context of semigroup theory a fundamental field of study in algebra. Quasi covered ideals represent a novel subset of semigroups, offering a versatile perspective that extends beyond conventional ideals, enabling a more flexible analysis of semigroup structures. In this paper, we delve into the properties and attributes of quasi covered ideals, providing a comprehensive exploration of their characteristics. Additionally, we establish intricate relationship between covered ideals, the greatest ideal, quasi covered ideals, and quasi bases, shedding light on the interconnections among these fundamental elements within the realm of semigroup theory. [ABSTRACT FROM AUTHOR]

Let = Tri(A,M, B) be a triangular algebra. In this paper, we prove that under certain conditions, every local derivation from - into itself is a derivation; every additive 2-local Lie derivation from - into itself is a Lie derivation. [ABSTRACT FROM AUTHOR]

In this paper, we connect four different branches of Mathematics: Statistics, Probability, Algebra and Discrete Mathematics with the objective of introducing new results on Markov chains and evolution algebras obtained by following a relatively new line of research, already dealt with by several authors. It consists of the use of certain directed graphs to facilitate the study of Markov chains and evolution algebras, as well as to use each of the three objects to make easier the study of the other two. The results obtained can be useful, in turn, to link different scientific disciplines, such as Physics, Engineering and Mathematics, in which evolution algebras are considered very interesting tools. [ABSTRACT FROM AUTHOR]

This paper explores several topics related to Woodin's HOD conjecture. We improve the large cardinal hypothesis of Woodin's HOD dichotomy theorem from an extendible cardinal to a strongly compact cardinal. We show that assuming there is a strongly compact cardinal and the HOD hypothesis holds, there is no elementary embedding from HOD to HOD, settling a question of Woodin. We show that the HOD hypothesis is equivalent to a uniqueness property of elementary embeddings of levels of the cumulative hierarchy. We prove that the HOD hypothesis holds if and only if every regular cardinal above the first strongly compact cardinal carries an ordinal definable ω -Jónsson algebra. We show that if the HOD hypothesis holds and HOD satisfies the Ultrapower Axiom, then every supercompact cardinal is supercompact in HOD. [ABSTRACT FROM AUTHOR]

In this paper, we first define the pre-Lie family algebra associated to a dendriform family algebra in the case of a commutative semigroup. Then we construct a pre-Lie family algebra via typed decorated rooted trees, and we prove the freeness of this pre-Lie family algebra. We also construct pre-Lie family operad in terms of typed labeled rooted trees, and we obtain that the operad of pre-Lie family algebras is isomorphic to the operad of typed labeled rooted trees, which generalizes the result of Chapoton and Livernet. In the end, we construct Zinbiel and pre-Poisson family algebras and generalize results of Aguiar. [ABSTRACT FROM AUTHOR]

An endomorphism of a finite algebra is said to be highest if its pre-period is greater than or equal to the pre-period of all its endomorphisms. In this paper, we characterize all highest endomorphisms of a Boolean lattice. [ABSTRACT FROM AUTHOR]

Vibration measurements can be used to evaluate the operation status of power equipment and are widely applied in equipment quality inspection and fault identification. Event-sensing technology can sense the change in surface light intensity caused by object vibration and provide a visual description of vibration behavior. Based on the analysis of the principle underlying the transformation of vibration behavior into event flow data by an event sensor, this paper proposes an algorithm to reconstruct event flow data into a relationship correlating vibration displacement and time to extract the amplitude-frequency characteristics of the vibration signal. A vibration measurement test platform is constructed, and feasibility and effectiveness tests are performed for the vibration motor and other power equipment. The results show that event-sensing technology can effectively perceive the surface vibration behavior of power and provide a wide dynamic range. Furthermore, the vibration measurement and visualization algorithm for power equipment constructed using this technology offers high measurement accuracy and efficiency. The results of this study provide a new noncontact and visual method for locating vibrations and performing amplitude-frequency analysis on power equipment. [ABSTRACT FROM AUTHOR]

Copyright of Crítica is the property of Instituto de Investigaciones Filosoficas and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Two mathematical fields that concentrate on creating and analyzing structures are algebra and graph theory. There are numerous studies linking algebraic structures like groups, rings, fields and vector spaces with graph theory. Several algebraic graphs have been defined based on the properties of the order of the group and its elements. In this paper, we systematically review the literature on such graphs to understand the research dynamics in the field. [ABSTRACT FROM AUTHOR]

A degree one element of the Orlik-Solomon algebra of a hyperplane arrangement defines a cochain complex known as the Aomoto complex. The Aomoto complex can be considered as the "linear approximation" of the twisted cochain complex with coefficients in a complex rank one local system. In this paper, we discuss q-deformations of the Aomoto complex. The q-deformation is defined by replacing the entries of representation matrices of the coboundary maps with their q-analogues. While the resulting maps do not generally define cochain complexes, for certain special basis derived from real structures, the q-deformation becomes again a cochain complex. Moreover, it exhibits universality in the sense that any specialization of q to a complex number yields the cochain complex computing the corresponding local system cohomology group. [ABSTRACT FROM AUTHOR]

In the literature on Kleene algebra, a number of variants have been proposed which impose additional structure specified by a theory, such as Kleene algebra with tests (KAT) and the recent Kleene algebra with observations (KAO), or make specific assumptions about certain constants, as for instance in NetKAT. Many of these variants fit within the unifying perspective offered by Kleene algebra with hypotheses, which comes with a canonical language model constructed from a given set of hypotheses. For the case of KAT, this model corresponds to the familiar interpretation of expressions as languages of guarded strings. A relevant question therefore is whether Kleene algebra together with a given set of hypotheses is complete with respect to its canonical language model. In this paper, we revisit, combine and extend existing results on this question to obtain tools for proving completeness in a modular way. We showcase these tools by giving new and modular proofs of completeness for KAT, KAO and NetKAT, and we prove completeness for new variants of KAT: KAT extended with a constant for the full relation, KAT extended with a converse operation, and a version of KAT where the collection of tests only forms a distributive lattice. [ABSTRACT FROM AUTHOR]

Operated algebras, that is, algebras equipped with linear operators, have important applications in mathematics and physics. Two primary instances of operated algebras are the Rota–Baxter algebra and TD-algebra. In this paper, we introduce a λ -TD algebra that includes both the Rota–Baxter algebra and the TD-algebra. The explicit construction of free commutative λ -TD algebra on a commutative algebra is obtained by a generalized shuffle product, called the λ -TD shuffle product. We then show that the free commutative λ -TD algebra possesses a left counital bialgebra structure by means of a suitable 1-cocycle condition. Furthermore, the classical result that every connected filtered bialgebra is a Hopf algebra, is extended to the context of left counital bialgebras. Given this result, we finally prove that the left counital bialgebra on the free commutative λ -TD algebra is connected and filtered, and thus is a left counital Hopf algebra. [ABSTRACT FROM AUTHOR]

Action of a pomonoid on partially ordered sets (S -posets) has beautiful aspects in practical subjects such as automata theory, projection algebra and theoretical computer science which makes it always capture the interest of mathematicians. On the other hand, the study of different kinds of weakly injectivity (which category theory inherited from homological and commutative algebra) is an interesting subject for mathematicians. One of the important kinds of weakly injectivity is quasi-injectivity. In this paper, we study quasi-injectivity in the category of S -posets with respect to special kind of order embeddings, namely, down-closed embeddings (dc-quasi-injectivity). [ABSTRACT FROM AUTHOR]

In this paper, we continue the study of Hurwitz series over a commutative unital ring that was begun in [W. Keigher, On the ring of Hurwitz series, Commun. Algebra 25 (1997) 1845–1859; W. Keigher and F. Pritchard, Hurwitz series as formal functions, J. Pure Appl. Algebra 146 (2000) 291–304]. In particular, we introduce the notion of multivariate Hurwitz series. The underlying idea is that multivariate Hurwitz series are to Hurwitz series as studied in [W. Keigher, On the ring of Hurwitz series, Commun. Algebra 25 (1997) 1845–1859; W. Keigher and F. Pritchard, Hurwitz series as formal functions, J. Pure Appl. Algebra 146 (2000) 291–304] as formal power series in several indeterminates are to formal power series in only one indeterminate. The elementary aspects of the theory follow along the lines of [W. Keigher, On the ring of Hurwitz series, Commun. Algebra 25 (1997) 1845–1859; W. Keigher and F. Pritchard, Hurwitz series as formal functions, J. Pure Appl. Algebra 146 (2000) 291–304]. The treatment of substitution and divided powers introduces special problems not encountered in [W. Keigher and F. Pritchard, Hurwitz series as formal functions, J. Pure Appl. Algebra 146 (2000) 291–304] and requires special attention to subtle details. However, we are able to establish analogous results. With substitution and divided powers in place, we construct and study the analog to the so called inner transformations of [S. Bochner and W. T. Martin, Several Complex Variables (Princeton University Press, 1948)]. Finally, we are able to establish analogs to many of the fundamental results of single and multivariate calculus. [ABSTRACT FROM AUTHOR]

In this paper, we construct a holomorphic Siegel modular form of weight 2 and level 2, and compute its Fourier coefficients explicitly. Moreover, we prove that this modular form equals the generating function of the representative number ρ (n , m , r) associated with the maximal order in the quaternion algebra (− 1 , − 1) ℚ . As a corollary, we can give a new proof of the famous formula for the sums of three squares. As applications, we give an explicit formula for the numbers of solutions of two systems of Diophantine equations related with Sun's "1-3-5 conjecture". Furthermore, we show that "a perfect square" in the integral condition version of Sun's conjecture can be replaced by "a power of 4". [ABSTRACT FROM AUTHOR]

Copyright of Western Anatolia Journal of Educational Sciences (WAJES) / Batı Anadolu Eğitim Bilimleri Dergisi is the property of Dokuz Eylul University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, first, we introduce the notion of post-Hopf algebra, which gives rise to a post-Lie algebra on the space of primitive elements and the fact that there is naturally a post-Hopf algebra structure on the universal enveloping algebra of a post-Lie algebra. A novel property is that a cocommutative post-Hopf algebra gives rise to a generalized Grossman-Larson product, which leads to a subadjacent Hopf algebra and can be used to construct solutions to the Yang-Baxter equation. Then, we introduce the notion of relative Rota-Baxter operator on Hopf algebras. A cocommutative post-Hopf algebra gives rise to a relative Rota-Baxter operator on its subadjacent Hopf algebra. Conversely, a relative Rota-Baxter operator also induces a post-Hopf algebra. Finally, we show that relative Rota-Baxter operators give rise to matched pairs of Hopf algebras. Consequently, post-Hopf algebras and relative Rota-Baxter operators give solutions to the Yang-Baxter equation in certain cocommutative Hopf algebras. [ABSTRACT FROM AUTHOR]

Let K be a field, Q = (Q0, Q1) be a quiver and KQ be the generalised path algebra [10]. This paper gives a characterisation for the right and left modules over the path algebras of finite acyclic quiver. The study shows that the modules over such path algebras could be written as the decomposition of KQ-submodules. For KQ-modules over path algebras of quiver with countably many vertices, a sequence of KQ-submodules is identified which in finite case is a composition series. [ABSTRACT FROM AUTHOR]

In this paper, the  (2 + 1) -dimensional seventh-order Caudrey–Dodd–Gibbon–KP equation is investigated through the Lie group method. The Lie algebra of infinitesimal symmetries, commutative and adjoint tables, and one-dimensional optimal systems is presented. Then, the seventh-order Caudrey–Dodd–Gibbon–KP equation is reduced to nine types of  (1 + 1) -dimensional equations with the help of symmetry subalgebras. Finally, the unified algebra method is used to obtain the soliton solutions, trigonometric function solutions, and Jacobi elliptic function solutions of the seventh-order Caudrey–Dodd–Gibbon–KP equation. [ABSTRACT FROM AUTHOR]

Using the first cohomology from the mirror Heisenberg–Virasoro algebra to the twisted Heisenberg algebra (as the mirror Heisenberg–Virasoro algebra module), in this paper, we determined the derivations on the mirror Heisenberg–Virasoro algebra. Based on this result, we proved that any two-local derivation on the mirror Heisenberg–Virasoro algebra is a derivation. All half-derivations are described, and as corollaries, we have descriptions of transposed Poisson structures and local (two-local) half-derivations on the mirror Heisenberg–Virasoro algebra. [ABSTRACT FROM AUTHOR]

In this paper, we classify the derivations of degree-one generalized Weyl algebras over a univariate Laurent polynomial ring. In particular, our results cover the Weyl–Hayashi algebra, a quantization of the first Weyl algebra arising as a primitive factor algebra of U q + ( 5) , and a family of algebras which localize to the group algebra of the infinite group with generators x and y , subject to the relation x y = y − 1 x. [ABSTRACT FROM AUTHOR]

The present paper is devoted to studying local derivations on the Lie algebra $ W(2,2) $ W (2 , 2) which has some outer derivations. Using some linear algebra methods in [1] and a key construction for $ W(2,2) $ W (2 , 2) , we prove that every local derivation on $ W(2, 2) $ W (2 , 2) is a derivation. As an application, we determine all local derivations on the deformed $ \mathfrak {bms}_3 $ b m s 3 algebra. [ABSTRACT FROM AUTHOR]

A class of left bialgebroids whose underlying algebra A ♯ H is a smash product of a bialgebra H with a braided commutative Yetter–Drinfeld H -algebra A has recently been studied in relation to models of field theories on noncommutative spaces. In Borowiec and Pachoł (2017 J. Phys. A: Math. Theor. 50 055205) a proof has been presented that the bialgebroid A F ♯ H F where HF and AF are the twists of H and A by a Drinfeld 2-cocycle F = ∑ F 1 ⊗ F 2 is isomorphic to the twist of bialgebroid A ♯ H by the bialgebroid 2-cocycle ∑ 1 ♯ F 1 ⊗ 1 ♯ F 2 induced by F. They assume H is quasitriangular, which is reasonable for many physical applications. However the proof and the entire paper take for granted that the coaction and the prebraiding are both given by special formulas involving the R-matrix. There are counterexamples of Yetter–Drinfeld modules over quasitriangular Hopf algebras which are not of this special form. Nevertheless, the main result essentially survives. We present a proof with a general coaction and the correct prebraiding, and even without the assumption of quasitriangularity. [ABSTRACT FROM AUTHOR]

Given a directed graph E and a labeling ℒ, one forms the labeled graph C* -algebra by taking a weakly left--resolving labeled space (E, ℒ, 퓑) and considering a universal generating family of partial isometries and projections. In this paper, given a labeled space (E, ℒ, 퓑), we provide a process in which one can build a "larger" desingularized labeled space (F, ℒF, 퓑F) whose graph F essentially maintains the loop structure of the original graph E and such that the unitization of C*(E, ℒ, 퓑) is a full corner of C*(F, ℒF, 퓑F). [ABSTRACT FROM AUTHOR]

Let A be a unital simple separable infinite dimensional stably finite C*-algebra and B be a large subalgebra of A. In this paper, we show that B has (strong tracial or tracial) mcomparison of positive elements if A has (strong tracial or tracial) m-comparison of positive elements. [ABSTRACT FROM AUTHOR]

Profinite congruences on profinite algebras determining profinite quotients are difficult to describe. In particular, no constructive description is known of the least profinite congruence containing a given binary relation on the algebra. On the other hand, closed congruences and fully invariant congruences can be described constructively. In a previous paper, we conjectured that fully invariant closed congruences on a relatively free profinite algebra are always profinite. Here, we show that our conjecture fails for unary algebras and that closed congruences on relatively free profinite semigroups are not necessarily profinite. As part of our study of unary algebras, we establish an adjunction between profinite unary algebras and profinite monoids. We also show that the Polish representation of the free profinite unary algebra is faithful. [ABSTRACT FROM AUTHOR]

Let (A,\mathfrak {m}) be an excellent normal domain of dimension two containing a field k \cong A/\mathfrak {m}. An \mathfrak {m}-primary ideal I is a p_g-ideal if the Rees algebra A[It] is a Cohen-Macaulay normal domain. If k is algebraically closed then Okuma, Watanabe and Yoshida proved that A has p_g-ideals and furthermore product of two p_g-ideals is a p_g ideal. Previously we showed that if k has characteristic zero then A has p_g-ideals. In this paper we prove that if k is perfect field of positive characteristic then also A has p_g ideals. [ABSTRACT FROM AUTHOR]

In this paper, we develop a braid theoretic approach for computing the Kauffman bracket skein module of the lens spaces L (p , q) , KBSM(L (p , q)), for q ≠ 0. For doing this, we introduce a new concept, that of an unoriented braid. Unoriented braids are obtained from standard braids by ignoring the natural top-to-bottom orientation of the strands. We first define the generalized Temperley–Lieb algebra of type B, TL 1 , n , which is related to the knot theory of the solid torus ST, and we obtain the universal Kauffman bracket-type invariant, V , for knots and links in ST, via a unique Markov trace constructed on TL 1 , n . The universal invariant V is equivalent to the KBSM(ST). For passing now to the KBSM(L (p , q)), we impose on V relations coming from the band moves (or slide moves), that is, moves that reflect isotopy in L (p , q) but not in ST, and which reflect the surgery description of L (p , q) , obtaining thus, an infinite system of equations. By construction, solving this infinite system of equations is equivalent to computing KBSM(L (p , q)). We first present the solution for the case q = 1 , which corresponds to obtaining a new basis, ℬ p , for KBSM(L (p , 1)) with (⌊ p / 2 ⌋ + 1) elements. We note that the basis ℬ p is different from the one obtained by Hoste and Przytycki. For dealing with the complexity of the infinite system for the case q > 1 , we first show how the new basis ℬ p of KBSM(L (p , 1)) can be obtained using a diagrammatic approach based on unoriented braids, and we finally extend our result to the case q > 1. The advantage of the braid theoretic approach that we propose for computing skein modules of c.c.o. 3-manifolds, is that the use of braids provides more control on the isotopies of knots and links in the manifolds, and much of the diagrammatic complexity is absorbed into the proofs of the algebraic statements. [ABSTRACT FROM AUTHOR]