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Abstract Some cases of the LFED Conjecture, proposed by the second author [15] , for certain integral domains are proved. In particular, the LFED Conjecture is completely established for the field of fractions k (x) of the polynomial algebra k [ x ] , the formal power series algebra k [ [ x ] ] and the Laurent formal power series algebra k [ [ x ] ] [ x − 1 ] , where x = (x 1 , x 2 , ... , x n) denotes n commutative free variables and k a field of characteristic zero. Furthermore, the relation between the LFED Conjecture and the Duistermaat–van der Kallen Theorem [3] is also discussed and emphasized. [ABSTRACT FROM AUTHOR]

Abstract We study the differential identities of the algebra U T 2 of 2 × 2 upper triangular matrices over a field of characteristic zero. We let the Lie algebra L = Der (U T 2) of derivations of U T 2 (and its universal enveloping algebra) act on it. We study the space of multilinear differential identities in n variables as a module for the symmetric group S n and we determine the decomposition of the corresponding character into irreducibles. If V is the variety of differential algebras generated by U T 2 , we prove that unlike the other cases (ordinary identities, group graded identities) V does not have almost polynomial growth. Nevertheless we exhibit a subvariety U of V having almost polynomial growth. [ABSTRACT FROM AUTHOR]

Abstract Given a finite group G , we say that G has property P n if for every prime integer p , G has at most n − 1 irreducible characters whose degrees are multiples of p. In this paper, we classify all finite groups that have property P 4. We show that the groups satisfying property P 4 are exactly the finite groups with at most three nonlinear irreducible characters, one solvable group of order 168, SL 2 (3) , A 5 , S 5 , PSL 2 (7) and A 6. [ABSTRACT FROM AUTHOR]

Abstract Let R ⊆ Q be rings such that the inclusion φ : R → Q is an epimorphism in the category of rings and Q is flat both as a right and as a left R -module. Assume that F. dim (Q Q ) = 0 , that is, that every left Q -module has projective dimension 0 or ∞. We prove that the following conditions are equivalent: (i) Flat left R -modules are strongly flat. (ii) Matlis-cotorsion left R -modules are Enochs-cotorsion. (i i i) h -divisible left R -modules are weak-injective. (iv) Homomorphic images of weak-injective left R -modules are weak-injective. (v) Homomorphic images of injective left R -modules are weak-injective. (vi) Left R -modules of weak dimension ≤1 are of projective dimension ≤1. (vii) The cotorsion pairs (P 1 , H D) and (F 1 , W I) coincide. Moreover, if R is a right and left Ore ring, S is its set of regular elements and Q = R [ S − 1 ] = [ S − 1 ] R is the classical ring of quotients of R , then the seven conditions above are also equivalent to: (v i i i) Divisible left R -modules are weak-injective. This extends a result by Fuchs and Salce (2018) [10] for modules over a commutative ring R. [ABSTRACT FROM AUTHOR]

Let C 2 be the group of order 2. We prove K 2 ( Z [ C 2 × C 2 ] ) is isomorphic to ( Z / 2 ) 6 and give an F 2 -basis of it. As an application, we show W h 2 ( C 2 × C 2 ) is isomorphic to ( Z / 2 ) 2 . [ABSTRACT FROM AUTHOR]

Abstract: The ramification filtration on the compositum of two wildly ramified extensions is computed in various cases. Some positive results towards Abhyankar's inertia conjecture have been also proved. [Copyright &y& Elsevier]

Abstract: We study symbolic powers of bi-homogeneous ideals of points in and extend to this setting results on the effect of points fattening obtained in [2] and [4]. We prove a Chudnovsky-type theorem for bi-homogeneous ideals and apply it to classification of configurations of points with minimal or no fattening effect. [Copyright &y& Elsevier]

Abstract: In 1995, Camillo and Yu showed that an exchange ring has stable range 1 if and only if every regular element is unit-regular. An element m in a module is called regular if for some . In this paper we define stable modules and show that if M has the finite exchange property then M is stable if and only if, for every regular element , where is epic (and we say that m is unit-regular). Such modules are called regular-stable. It is shown that is regular-stable if and only if R has internal cancellation. To simplify the exposition, many arguments are formulated in an arbitrary Morita context. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to give a characterization of maximal hyperelliptic curves over a finite field given by the equation . [Copyright &y& Elsevier]

Abstract: A group obtained from a nontrivial group by adding one generator and one relator which is a proper power of a word in which the exponent sum of the additional generator is one contains the free square of the initial group and almost always (with one obvious exception) contains a non-abelian free subgroup. If the initial group is involution-free or the relator is at least third power, then the obtained group is SQ-universal and relatively hyperbolic with respect to the initial group. [Copyright &y& Elsevier]

Abstract: In this short note, we give a formula for the restriction of multiplier ideals when their depth is greater than one. [Copyright &y& Elsevier]

Abstract: Let be a Garside group with Garside element , and let be the minimal positive central power of . An element is said to be periodic if some power of it is a power of . In this paper, we study periodic elements in Garside groups and their conjugacy classes. We show that the periodicity of an element does not depend on the choice of a particular Garside structure if and only if the center of is cyclic; if for some nonzero integer , then is conjugate to ; every finite subgroup of the quotient group is cyclic. By a classical theorem of Brouwer, Kerékjártó and Eilenberg, an -braid is periodic if and only if it is conjugate to a power of one of two specific roots of . We generalize this to Garside groups by showing that every periodic element is conjugate to a power of a root of . We introduce the notions of slimness and precentrality for periodic elements, and show that the super summit set of a slim, precentral periodic element is closed under any partial cycling. For the conjugacy problem, we may assume the slimness without loss of generality. For the Artin groups of type , , , and the braid group of the complex reflection group of type , endowed with the dual Garside structure, we may further assume the precentrality. [Copyright &y& Elsevier]

Abstract: Let , , be a general union of planes and lines. Here we prove that has the expected postulation if is small with respect to . [ABSTRACT FROM AUTHOR]

Abstract: Given a Lie bialgebra , we present an explicit procedure to construct coisotropic subalgebras, i.e. Lie subalgebras of whose annihilator is a Lie subalgebra of . We write down families of examples for the case that is a classical complex simple Lie algebra. [ABSTRACT FROM AUTHOR]

Abstract: We analyze Auslander–Reiten components for the bounded derived category of a finite-dimensional algebra. We classify derived categories whose Auslander–Reiten quiver has either a finite stable component or a stable component with finite Dynkin tree class or a bounded stable component. Their Auslander–Reiten quivers are determined. We also determine components that contain shift periodic complexes. [ABSTRACT FROM AUTHOR]

Abstract: We study the postulation of a general union of double, triple, and quartuple points of . We prove that has the expected postulation in degree , using the Horace differential lemma. We also discuss the cases of low degree with the aid of computer algebra. [Copyright &y& Elsevier]

Abstract: For a basic self-injective algebra which has an indecomposable standardly stratifying complement , we determine its quiver and some relations, and a kind of coarse structure. [Copyright &y& Elsevier]

Abstract: We show that the main results of Happel–Rickard–Schofield (1988) and Happel–Reiten–Smalø (1996) on piecewise hereditary algebras are coherent with the notion of group action on an algebra. Then, we take advantage of this compatibility and show that if is a finite group acting on a piecewise hereditary algebra over an algebraically closed field whose characteristic does not divide the order of , then the resulting skew group algebra is also piecewise hereditary. [Copyright &y& Elsevier]

Abstract: In this paper, the cellularity of twisted semigroup algebras over an integral domain is investigated by introducing the concept of cellular twisted semigroup algebras of type . Partition algebras, Brauer algebras and Temperley–Lieb algebras all are examples of cellular twisted semigroup algebras of type . Our main result shows that the twisted semigroup algebra of a regular semigroup is cellular of type with respect to an involution on the twisted semigroup algebra if and only if the twisted group algebras of certain maximal subgroups are cellular algebras. Here we do not assume that the involution of the twisted semigroup algebra induces an involution of the semigroup itself. Moreover, for a twisted semigroup algebra, we do not require that the twisting decomposes essentially into a constant part and an invertible part, or takes values in the group of units in the ground ring. Note that trivially twisted semigroup algebras are the usual semigroup algebras. So, our results extend not only a recent result of East, but also some results of Wilcox. [Copyright &y& Elsevier]

Abstract: We give some conditions for objects to be what we call a “cohomologically Schurian set of generators” for the bounded derived category (-mod) of a finite-dimensional algebra . For any such set of generators, we construct a -structure on (-mod), which has these objects as its simple objects. If is self-injective, we prove that the heart of this -structure is equivalent to a module category. To prove this fact we prove that the heart has an injective cogenerator. [Copyright &y& Elsevier]

Abstract: We characterize the maximum -local index of a Schur algebra over an abelian number field in terms of global information determined by the field for an arbitrary rational prime, . This completes and unifies previous results of Janusz in [G.J. Janusz, The Schur group of an algebraic number field, Ann. of Math. (2) 103 (1976) 253–281] and Pendergrass in [J.W. Pendergrass, The 2-part of the Schur group, J. Algebra 41 (1976) 422–438]. [Copyright &y& Elsevier]

Abstract: We show that a maximal curve over given by an equation , where is additive and separable and where has degree prime to the characteristic , is such that all roots of belong to . In the particular case where , we show that the degree is a divisor of . [Copyright &y& Elsevier]

Abstract: We present two examples of distributive algebraic lattices which are not isomorphic to the congruence lattice of any lattice. The first such example was discovered by F. Wehrung in 2005. One of our examples is defined topologically, the other one involves majority algebras. In particular, we prove that the congruence lattice of the free majority algebra on (at least) generators is not isomorphic to the congruence lattice of any lattice. Our method is a generalization of Wehrung’s approach, so that we are able to apply it to a larger class of distributive semilattices. [Copyright &y& Elsevier]

Abstract: We determine all types and canonical forms of simple subalgebras for each type of special simple Jordan algebras over an algebraically closed field of characteristic not equal to 2, as well as a number of conjugacy classes. [Copyright &y& Elsevier]

Abstract: We describe new types of normal forms for braid monoids, Artin–Tits monoids, and, more generally, for all monoids in which divisibility has some convenient lattice properties (“locally Garside monoids”). We show that, in the case of braids, one of these normal forms coincides with the normal form introduced by Burckel and deduce that the latter can be computed easily. This approach leads to a new, simple description for the standard order (“Dehornoy order”) of in terms of that of , and to a quadratic upper bound for the complexity of this order. [Copyright &y& Elsevier]

Abstract: The maximal subalgebras of the finite-dimensional simple special Jordan superalgebras over an algebraically closed field of characteristic 0 are studied. This is a continuation of a previous paper by the same authors about maximal subalgebras of simple associative superalgebras, which is instrumental here. [Copyright &y& Elsevier]

Abstract: This note elaborates on Th. Voronov’s construction [Th. Voronov, Higher derived brackets and homotopy algebras, J. Pure Appl. Algebra 202 (1–3) (2005) 133–153; Th. Voronov, Higher derived brackets for arbitrary derivations, Travaux Math. XVI (2005) 163–186] of -structures via higher derived brackets with a Maurer–Cartan element. It is shown that gauge equivalent Maurer–Cartan elements induce -isomorphic structures. Applications in symplectic, Poisson and Dirac geometry are discussed. [Copyright &y& Elsevier]

Abstract: Let be linearly independent homogeneous polynomials in the standard -graded ring with the same degree and no common divisors. This defines a morphism . The Rees algebra of the ideal is the graded -algebra which can be described as the image of an -algebra homomorphism : . This paper discusses one result concerning the structure of the kernel of the map and its relation to the problem of finding the implicit equation of the image of the map given by , , . In particular, we prove a conjecture of Hong, Simis and Vasconcelos. We also relate our results to the theory of adjoint curves and prove a special case of a conjecture of Cox. [Copyright &y& Elsevier]

Abstract: The only known examples of Anosov diffeomorphisms are hyperbolic automorphisms of infranilmanifolds, and the existence of such automorphisms is a really strong condition on the rational nilpotent Lie algebra determined by the lattice, so called an Anosov Lie algebra. We prove that ( times, ) has an Anosov rational form for any graded real nilpotent Lie algebra having a rational form. We also obtain some obstructions for the types of nilpotent Lie algebras allowed, and use the fact that the eigenvalues of the automorphism are algebraic integers (even units) to show that the types and are not possible for Anosov Lie algebras. [Copyright &y& Elsevier]

Abstract: Let be a fat point scheme in supported on general points. Here we prove that if the multiplicities are at most 3 and the length of is sufficiently high then the number of generators of the homogeneous ideal in each degree is as small as numerically possible. Since it is known that has maximal Hilbert function, this implies that has the expected minimal free resolution. [Copyright &y& Elsevier]

Abstract: Let be a commutative -algebra, where is an algebraically closed field of characteristic , and let be an -module. We consider the following question: Under what conditions is it possible to find a connection on ? We consider the maximal Cohen–Macaulay (MCM) modules over complete CM algebras that are isolated singularities, and usually assume that the singularities have finite CM representation type. It is known that any MCM module over a simple singularity of dimension admits an integrable connection. We prove that an MCM module over a simple singularity of dimension admits a connection if and only if it is free. Among singularities of finite CM representation type, we find examples of curves with MCM modules that do not admit connections, and threefolds with non-free MCM modules that admit connections. Let be a singularity not necessarily of finite CM representation type, and consider the condition that is a Gorenstein curve or a -Gorenstein singularity of dimension . We show that this condition is sufficient for the canonical module to admit an integrable connection, and conjecture that it is also necessary. In support of the conjecture, we show that if is a monomial curve singularity, then the canonical module admits an integrable connection if and only if is Gorenstein. [Copyright &y& Elsevier]

Abstract: Let be a graded algebra over a field such that is a finite product of copies of and each is finite dimensional over . Set and . We study the properties of the categories of graded -modules and -modules that relate to the noetherianity of . We pay particular attention to the case when is a Koszul algebra and is the Koszul dual to . [Copyright &y& Elsevier]

Abstract: We show that any fat point (local punctual scheme) has at most one embedding in the affine space up to analytic equivalence. If the algebra of functions of the fat point admits a non-trivial grading over the non-negative integers, we prove that it has at most one embedding up to algebraic equivalence. However, we give an example of a fat point having algebraically non-equivalent embeddings in the affine plane. [Copyright &y& Elsevier]

Abstract: In this paper we define model solvmanifold pairs and their diagonal type selfmaps in the tradition of Heath and Keppelmann. We derive an explicit formula for computing the relative Nielsen number on these spaces and selfmaps . We find that model solvmanifold pairs often exhibit interesting Schirmer theory, meaning . [Copyright &y& Elsevier]

Abstract: The Alexander–Hirschowitz theorem says that a general collection of double points in imposes independent conditions on homogeneous polynomials of degree with a well-known list of exceptions. Alexander and Hirschowitz completed its proof in 1995, solving a long standing classical problem, connected with the Waring problem for polynomials. We expose a self-contained proof based mainly on the previous works by Terracini, Hirschowitz, Alexander and Chandler, with a few simplifications. We claim originality only in the case , where our proof is shorter. We end with an account of the history of the work on this problem. [Copyright &y& Elsevier]

Abstract: We introduce a new class of algebras, the Nakayama oriented pullbacks, obtained from pullbacks of surjective morphisms of algebras and . We prove that such a pullback is tilted when and are hereditary. We also show that stably hereditary algebras respecting the clock condition are Nakayama oriented pullbacks, and we use results about these pullbacks to show when a stably hereditary algebra is tilted or iterated tilted. [Copyright &y& Elsevier]

Abstract: Let be a finite polynomial mapping of algebraic subsets of and , respectively, with . It is known that can be extended to a finite polynomial mapping . Moreover, it is known that, if are smooth of dimension , and is dominated on every component (without vertical components) then there exists a finite polynomial extension such that , where means the number of points in the generic fiber of . In this note we improve this result. Namely we show that there exists a finite polynomial extension such that . [Copyright &y& Elsevier]

Abstract: The Carlitz -algebra , , is generated over an algebraically closed field (which contains a non-discrete locally compact field of positive characteristic , i.e. , ), by the (power of the) Frobenius map , and by the Carlitz derivative . It is proved that the Krull and global dimensions of are 2, classifications of simple -modules and ideals are given, there are only countably many ideals, they commute , and each ideal is a unique product of maximal ones. It is a remarkable fact that any simple -module is a sum of eigenspaces of the element (the set of eigenvalues for is given explicitly for each simple -module). This fact is crucial in finding the group of -algebra automorphisms of and in proving that any two distinct Carlitz rings are not isomorphic ( if ). The centre of is found explicitly, it is a UFD that contains countably many elements. [Copyright &y& Elsevier]

Abstract: We show that every Kac–Moody Lie algebra of indefinite type contains a subalgebra with a Dynkin diagram having two adjacent vertices whose edge labels multiply to a number greater than or equal to five. Consequently, every Kac–Moody algebra of indefinite type contains a subalgebra of strictly hyperbolic type, and a free Lie algebra of rank two. [Copyright &y& Elsevier]

Abstract: Using Du’s characterization of the dual canonical basis of the coordinate ring , we express all elements of this basis in terms of immanants. We then give a new factorization of permutations avoiding the patterns 3412 and 4231, which in turn yields a factorization of the corresponding Kazhdan–Lusztig basis elements of the Hecke algebra . Using the immanant and factorization results, we show that for every totally nonnegative immanant and its expansion with respect to the basis of Kazhdan–Lusztig immanants, the coefficient must be nonnegative when avoids the patterns 3412 and 4231. [Copyright &y& Elsevier]

Abstract: We generalize the main theorem of Rieffel for Morita equivalence of -algebras to the case of unital dual operator algebras: two unital dual operator algebras have completely isometric normal representations such that and for a ternary ring of operators (i.e. a linear space such that ) if and only if there exists an equivalence functor which “extends” to a -functor implementing an equivalence between the categories and . By we denote the category of normal representations of and by the category with the same objects as and -module maps as morphisms (). We prove that this functor is equivalent to a functor “generated” by a bimodule, and that it is normal and completely isometric. [Copyright &y& Elsevier]

Abstract: We characterize algebras admitting two well-agreeing near weights. These algebras can be used for constructing error-correcting codes of algebraic geometric type over two points, by using elementary methods only. [Copyright &y& Elsevier]

Abstract: The aim of this article is to translate the well-known tensor product of representations of a group given by diagonal action to the case of representations of a quiver. We provide three different approaches and exhibit their close relationship to the point-wise tensor product, which is considered in [M. Herschend, Solution to the Clebsch–Gordan problem for Kronecker representations. U.U.D.M Project Report 2003:P1, Uppsala University, 2003; M. Herschend, Solution to the Clebsch–Gordan problem for representations of quivers of type , J. Algebra Appl. 4 (5) (2005) 481–488; M. Herschend, On the Clebsch–Gordan problem for quiver representations. U.U.D.M Report 2005:43, Uppsala University, 2005]. [Copyright &y& Elsevier]

Abstract: A finite poset carries a natural structure of a topological space. Fix a field , and denote by the bounded derived category of sheaves of finite dimensional -vector spaces over . Two posets and are said to be derived equivalent if and are equivalent as triangulated categories. We give explicit combinatorial properties of which are invariant under derived equivalence; among them are the number of points, the -congruency class of the incidence matrix, and the Betti numbers. We also show that taking opposites and products preserves derived equivalence. For any closed subset , we construct a strongly exceptional collection in and use it to show an equivalence for a finite dimensional algebra (depending on ). We give conditions on and under which becomes an incidence algebra of a poset. We deduce that a lexicographic sum of a collection of posets along a bipartite graph is derived equivalent to the lexicographic sum of the same collection along the opposite . This construction produces many new derived equivalences of posets and generalizes other well-known ones. As a corollary we show that the derived equivalence class of an ordinal sum of two posets does not depend on the order of summands. We give an example that this is not true for three summands. [Copyright &y& Elsevier]

Abstract: Let be a hereditary abelian -category with tilting object and denote the bounded derived category of . This paper is devoted to a study of suspended subcategories of by means of their Ext-projectives. [Copyright &y& Elsevier]

Abstract: Let be an Artin algebra. A pair of -modules is tilting provided that and are (finitely generated) self-orthogonal, and . Particularly, is a tilting module if and only if is a tilting pair. In the note, we will extend the Auslander–Reiten correspondence for tilting modules to the context of tilting pairs. [Copyright &y& Elsevier]

Abstract: A simply connected topological space has homotopy Lie algebra . Following Quillen, there is a connected differential graded free Lie algebra (dgL) called a Lie model, which determines the rational homotopy type of , and whose homology is isomorphic to the homotopy Lie algebra. We show that such a Lie model can be replaced with one that has a special property that we call being separated. The homology of a separated dgL has a particular form which lends itself to calculations. [Copyright &y& Elsevier]

Abstract: A tetrahedral curve is a (usually nonreduced) curve in defined by an unmixed, height two ideal generated by monomials. We characterize when these curves are arithmetically Cohen–Macaulay by associating a graph with each curve and, using results from combinatorial commutative algebra and Alexander duality, relating the structure of the complementary graph to the Cohen–Macaulay property. [Copyright &y& Elsevier]

Abstract: In this paper we study the adjoint functors between the category of Rota–Baxter algebras and the categories of dendriform dialgebras and trialgebras. In analogy to the well-known theory of the adjoint functor between the category of associative algebras and Lie algebras, we first give an explicit construction of free Rota–Baxter algebras and then apply it to obtain universal enveloping Rota–Baxter algebras of dendriform dialgebras and trialgebras. We further show that free dendriform dialgebras and trialgebras, as represented by binary planar trees and planar trees, are canonical subalgebras of free Rota–Baxter algebras. [Copyright &y& Elsevier]

Abstract: We define derived equivalent invariants for gentle algebras, constructed in an easy combinatorial way from the quiver with relations defining these algebras. Our invariants consist of pairs of natural numbers and contain important information about the algebra and the structure of the stable Auslander–Reiten quiver of its repetitive algebra. As a by-product we obtain that the number of arrows of the quiver of a gentle algebra is invariant under derived equivalence. Finally, our invariants separate the derived equivalence classes of gentle algebras with at most one cycle. [Copyright &y& Elsevier]