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We study symmetry properties and the possibility of exact integration of Klein–Gordon equations in external electromagnetic fields on 3D de Sitter background dS3. We present an algorithm for constructing the first-order symmetry algebra and describe its structure in terms of Lie algebra extensions. Based on the well-known classification of the subalgebras of the algebra s o (1 , 3) , we classify all electromagnetic fields on dS3 for which the corresponding Klein–Gordon equations admit first-order symmetry algebras. Then, we select the integrable cases, and for each of them, we construct exact solutions using the noncommutative integration method developed by Shapovalov and Shirokov [Theor. Math. Phys. 104, 921–934 (1995)]. We also propose an original algebraic method for constructing the special local coordinates on de Sitter space dS3, in which basis vector fields for subalgebras of the Lie algebra s o (1 , 3) have the simplest form. [ABSTRACT FROM AUTHOR]

Continuing the work of Monnier [Israel J. Math. 129, 189–207 (2002)], we determine the Gerstenhaber algebra structure over the Poisson cohomology groups for a large class of Poisson structures with isolated singularities over the plane. It reveals that there exists a GAGA-type phenomenon. We give an explicit description via generators and relations for the case of simple singularities. [ABSTRACT FROM AUTHOR]

We consider the problem of variable separation for the classical integrable Hamiltonian systems possessing gl(n)-valued Lax matrices satisfying quadratic Poisson brackets of Freidel and Maillet [Phys. Lett. B 262(2-3), 278 (1991)] with spectral-parameter dependent a-b-c-d tensors. We formulate, in terms of the corresponding a-b-c-d tensors, a sufficient condition that guarantees that the separating functions A(u), B(u) of Sklyanin [Commun. Math. Phys. 150(1), 181 (1992)], Scott [e-print arXiv:hep-th 940303 (1994)], and Gekhtman [Commun. Math. Phys. 167, 593 (1995)] produce canonical coordinates. We consider an important subcase of a-b-c-d algebras, namely, the case of classical reflection equation algebras [E. Sklyanin, J. Phys. A: Math. Gen. 21(10), 2357 (1988)], and formulate, in terms of the corresponding r-s-matrices, the analogous sufficient condition that guarantees the canonicity of the constructed coordinates. For the case s = 0, we recover our previous results on the variable separation for quadratic Sklyanin brackets [B. Dubrovin and T. Skrypnyk, J. Math. Phys. 60, 093506 (2019)]. We consider an example of gl(n) ⊗ gl(n)-valued trigonometric a-b-c-d tensors that satisfy the considered condition and find a class of Lax matrices for them for which the obtained set of canonical coordinates is complete. [ABSTRACT FROM AUTHOR]

We defined the notion of the quantum double inclusion [S. De, J. Math. Phys. 60, 071701 (2019)] associated with a finite-index and finite-depth subfactor, which is closely related to that of Ocneanu's asymptotic inclusion, and studied the quantum double inclusion associated with the Kac algebra subfactor RH ⊂ R, where H is a finite-dimensional Kac algebra acting outerly on the hyperfinite II1 factor R and RH denotes the fixed-point subalgebra. In this article, we analyze quantum double inclusions associated with the family of Kac algebra subfactors given by { R H ⊂ R ⋊ H ⋊ H * ⋊ ⋯ ︸ m times : m ≥ 1 }. For each m > 2, we construct a model N m ⊂ M for the quantum double inclusion of R H ⊂ R ⋊ H ⋊ H * ⋊ ⋯ ︸ m − 2 times , where N m = ((⋯ ⋊ H − 2 ⋊ H − 1 ) ⊗ ( H m ⋊ H m + 1 ⋊ ⋯ )) ′ ′ , M = (⋯ ⋊ H − 1 ⋊ H 0 ⋊ H 1 ⋊ ⋯ ) ′ ′ , and for any integer i, the notation Hi stands for H or H* according as i is odd or even. In this article, we give an explicit description of the subfactor planar algebra associated with N m ⊂ M (m > 2) which turns out to be a planar subalgebra of P * (m) ( H m ) (the adjoint of the m-cabling of the planar algebra of Hm). We then show that for each m > 2, the depth of N m ⊂ M is always two. Observing that N m ⊂ M is reducible for all m > 2, we study in great detail the weak Kac algebra structure of the relative commutant ( N m ) ′ ∩ M 2 . [ABSTRACT FROM AUTHOR]

We reinvestigate the two different q-Witt algebras and construct their n-algebras. In one case, the super version is also presented. Moreover we investigate the central extensions and present the (super) q-Virasoro n-algebras for the n even case. We study a toy model for the q-Virasoro constraints. A q-Witt n-algebra is discussed in this model. [ABSTRACT FROM AUTHOR]

Because Einstein–Podolsky–Rosen states are well-defined on the Weyl algebra, their canonical cyclic representations are suitable for demonstrating the process of remote state preparation. Local projection-valued measurements and the corresponding recovery unitary operator are formulated in this representation, whereupon generalized equatorial states are prepared remotely and faithfully. [ABSTRACT FROM AUTHOR]

Six fine gradings on the real form e 6 , − 14 are described, precisely those ones coming from fine gradings on the complexified algebra. The universal grading groups are Z 2 3 × Z 3 2 , Z 2 6 , Z × Z 2 4 , Z 2 7 , Z × Z 2 5 , and Z 2 × Z 2 3 . [ABSTRACT FROM AUTHOR]

We give a simplified description of quantum affine algebras in their loop presentation. This description is related to Drinfeld's new realization via halves of vertex operators. We also define an idempotent version of the quantum affine algebra which is suitable for categorification. [ABSTRACT FROM AUTHOR]

Galilean conformal algebra (GCA) is an Inönü–Wigner (IW) contraction of a conformal algebra, while Newton–Hooke string algebra is an IW contraction of an Anti-de Sitter (AdS) algebra, which is the isometry of an AdS space. It is shown that the GCA is a boundary realization of the Newton–Hooke string algebra in the bulk AdS. The string lies along the direction transverse to the boundary, and the worldsheet is AdS2. The one-dimensional conformal symmetry so(2,1) and rotational symmetry so(d) contained in the GCA are realized as the symmetry on the AdS2 string worldsheet and rotational symmetry in the space transverse to the AdS2 in AdSd+2, respectively. It follows from this correspondence that 32 supersymmetric GCAs can be derived as IW contractions of superconformal algebras, psu(2,2|4), osp(8|4), and osp(8*|4). We also derive less supersymmetric GCAs from su(2,2|2), osp(4|4), osp(2|4), and osp(8*|2). [ABSTRACT FROM AUTHOR]

We consider integrable open spin chains related to the quantum affine algebras Uq(o(3)) and Uq(A2(2)). We discuss the symmetry algebras of these chains with the local C3 space related to the Birman–Wenzl–Murakami algebra. The symmetry algebra and the Birman–Wenzl–Murakami algebra centralize each other in the representation space H=x1NC3 of the system, and this determines the structure of the spin system spectra. Consequently, the corresponding multiplet structure of the energy spectra is obtained. [ABSTRACT FROM AUTHOR]

The need to consider n-ary algebraic structures, generalizing Lie and Poisson algebras, has become increasingly important in physics, and it should therefore be of interest to study the mathematical concepts related to n-ary algebras. The purpose of this paper is to investigate ternary multiplications (as deformations of n-Lie structures) constructed from the binary multiplication of a Hom–Lie algebra, a linear twisting map, and a trace function satisfying certain compatibility conditions. We show that the relation between the kernels of the twisting maps and the trace function plays an important role in this context and provide examples of Hom–Nambu–Lie algebras obtained using this construction. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of weak solutions of the coupled time-dependent Ginzburg-Landau equations and establish the global existence of weak solutions to the equations by Galerkin method and compactness theory. [ABSTRACT FROM AUTHOR]

We study classes of indecomposable representations of the Diamond Lie algebra: a four-dimensional solvable Lie algebra, which is the central extension of the Poincaré Lie algebra in two dimensions. These representations are obtained first (inspired by Douglas and Premat [Commun. Algebra 35, 1433 (2007)]) by embedding the Diamond Lie algebra in the simple Lie algebras A2 and C2, and then by regarding it as a subalgebra of a truncated current Lie algebra. [ABSTRACT FROM AUTHOR]

We study limiting cases of the two known integrable chiral-type models with three-dimensional configuration space. One of the initial models is the non-Abelian Toda A2(1) model and the other was found by means of the symmetry approach by Meshkov and Demskoi [Theor. Math. Phys. 134, 351 (2003)]. The C-integrability of the reduced models is established by constructing their complete sets of integrals and general solutions. A description of the generalized symmetry algebras of these models is given in terms of operator mapping integrals into symmetries. The integrals of the Liouville-type systems are known to define Miura-type transformations for their generalized symmetries. This fact allowed us to find a few new systems of the Yajima–Oikawa type. We present a recursion operator for one them. [ABSTRACT FROM AUTHOR]

We study the final state problem for the nonlinear Klein–Gordon equation, utt+u-uxx=μu3, t∈R,x∈R, where μ∈R. We prove the existence of solutions in the neighborhood of the approximate solutions 2 Re U(t)w+(t), where U(t) is the free evolution group defined by U(t)=F-1e-it〈ξ〉F, =1+x2, F and F-1 are the direct and inverse Fourier transformations, respectively, and w+(t,x)=F-1(u⁁+(ξ)e(3/2)iμ〈ξ〉2|u⁁+(ξ)|2log t), with a given final data u+ is a real-valued function and |〈ξ〉3u⁁+(ξ)|L∞ is small. [ABSTRACT FROM AUTHOR]

The recently developed theory of quasi-Lie schemes is studied and applied to investigate several equations of Emden type and a scheme to deal with them and some of their generalizations is given. As a first result we obtain t-dependent constants of the motion for particular instances of Emden equations by means of some of their particular solutions. Previously known results are recovered from this new perspective. Some t-dependent constants of the motion for equations of Emden type satisfying certain conditions are recovered. Finally new exact particular solutions are given for certain cases of Emden equations. [ABSTRACT FROM AUTHOR]

This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloning on effect algebras and hidden variables. [ABSTRACT FROM AUTHOR]

It is shown that the coupled Volterra system governed by two-coupled nonlinear partial differential–difference equations (PDΔEs) has many integrability properties such as Lax representation, infinitely many generalized (nonpoint) symmetries and polynomial conserved densities, and a recursion operator. A systematic investigation on the continuous point symmetries of the coupled Volterra system shows that it admits a three dimensional nilpotent Lie algebra. By exploiting the obtained continuous point symmetries a similarity reduction is obtained. [ABSTRACT FROM AUTHOR]

We classify Lie n-algebras possessing an invariant Lorentzian inner product. [ABSTRACT FROM AUTHOR]

We introduce an extension of the character expansion method to the case of supergroups. This method allows us to calculate a superversion of the Leutwyler–Smilga integral which, to the best of our knowledge, has not been calculated before. We also use the method to generalize a previously calculated superversion of the Berezin–Karpelevich integral. Our character expansion method should also allow for the calculation of other supergroup integrals. [ABSTRACT FROM AUTHOR]

In 1940, Ulam proposed the famous Ulam stability problem. In this paper we introduce a general Cauchy–Jensen functional equation and prove the generalized Ulam stability of C*-ternary homomorphisms and C*-ternary derivations in C*-ternary algebras for the general Cauchy–Jensen equation. [ABSTRACT FROM AUTHOR]

We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated with a matrix, the representation theory can be understood in terms of “loop” and “string” representations, which are closely related to the dynamics of an iterated map in the plane. As a particular class of algebras, we introduce the “Hénon algebras,” for which the dynamical map is a generalized Hénon map, and give an example where irreducible representations of all dimensions exist. [ABSTRACT FROM AUTHOR]

The presented paper develops a new method for solving Einstein equations explicitly. Not only the solutions are new but also the mathematical framework of their construction which is given by a nonstandard function theory built over nonstandard algebras (in the following denoted as GAPs) and will be called here as “GAP Theory.” It is shown that the GAP theory succeeds in regions, where group theory fails: the group structure is too small to solve Einstein equations explicitly. [ABSTRACT FROM AUTHOR]

We compute necessary conditions on Yetter-Drinfeld modules over the groups SL(2,Fq) and GL(2,Fq) to generate finite dimensional Nichols algebras. This is a first step toward a classification of pointed Hopf algebras with a group of grouplikes isomorphic to one of these groups. [ABSTRACT FROM AUTHOR]

We show that for any bounded positive operator H with the simple spectrum, one can canonically define two coherent state maps. The algebras generated by annihilation operators defined by these coherent state maps are studied. We describe also how the Toda isospectral deformation of H deforms the corresponding coherent state maps and the related operator algebras. [ABSTRACT FROM AUTHOR]

We compute necessary conditions on Yetter-Drinfeld modules over the groups SL(2,Fq) and GL(2,Fq) to generate finite dimensional Nichols algebras. This is a first step toward a classification of pointed Hopf algebras with a group of grouplikes isomorphic to one of these groups. [ABSTRACT FROM AUTHOR]

In this paper, we first discuss the structure of the Ramond N=2 superconformal algebras. Then we classify the modules of the intermediate series over Ramond N=2 superconformal algebra. [ABSTRACT FROM AUTHOR]

We present an algorithm for characterizing the generalized Dirichlet to Neumann map for moving initial-boundary value problems. This algorithm is derived by combining the so-called global relation, which couples the initial and boundary values of the problem, with a new method for inverting certain one-dimensional integrals. This new method is based on the spectral analysis of an associated ordinary differantial equation and on the use of the d-bar formalism. As an illustration, the Neumann boundary value for the linearized Schrödinger equation is determined in terms of the Dirichlet boundary value and of the initial condition. [ABSTRACT FROM AUTHOR]

We find sets of solutions to the generalized spheroidal wave equation (GSWE) or, equivalently, to the confluent Heun equation. Each set is constituted by three solutions, one given by a series of ascending powers of the independent variable, and the others by series of regular and irregular confluent hypergeometric functions. For a fixed set, the solutions converge over different regions of the complex plane but present series coefficients proportional to each other. These solutions for the GSWE afford solutions to a double-confluent Heun equation by a taking-limit process due to Leaver. [E. W. Leaver, J. Math. Phys. 27, 1238 (1986)]. Another procedure, called Whittaker-Ince limit [B. D. Figueiredo, J. Math. Phys. 46, 113503 (2005)], provides solutions in series of powers and Bessel functions for two other equations with a different type of singularity at infinity. In addition, new solutions are obtained for the Whittaker-Hill and Mathieu equations [F. M. Arscott, Proc. R. Soc. Edinburg A67, 265 (1967)] by considering these as special cases of both the confluent and double-confluent Heun equations. In particular, we find that each of the Lindemann-Stieltjes solutions for the Mathieu equation [E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge University Press (1945)] is associated with two expansions in series of Bessel functions. We also discuss a set of solutions in series of hypergeometric and confluent hypergeometric functions for the GSWE and use their Leaver limits to obtain infinite-series solutions for the Schrödinger equation with an asymmetric double-Morse potential. Finally, the possibility of extending the solutions of the GSWE to the general Heun equation is briefly discussed. [ABSTRACT FROM AUTHOR]

Quantum entanglement was first recognized as a feature of quantum mechanics in the famous paper of Einstein, Podolsky, and Rosen. Recently it has been realized that quantum entanglement is a key ingredient in quantum computation, quantum communication, and quantum cryptography. In this paper, we introduce algebraic sets, which are determinantal varieties in the complex projective spaces or the products of complex projective spaces, for the mixed states on bipartite or multipartite quantum systems as their invariants under local unitary transformations. These invariants are naturally arised from the physical consideration of measuring mixed states by separable pure states. Our construction has applications in the following important topics in quantum information theory: (1) separability criterion, it is proved that the algebraic sets must be a union of the linear subspaces if the mixed states are separable; (2) simulation of Hamiltonians, it is proved that the simulation of semipositive Hamiltonians of the same rank implies the projective isomorphisms of the corresponding algebraic sets; (3) construction of bound entangled mixed states, examples of the entangled mixed states which are invariant under partial transpositions (thus PPT bound entanglement) are constructed systematically from our new separability criterion. [ABSTRACT FROM AUTHOR]

A relation between semidirect sums of Lie algebras and integrable couplings of lattice equations is established, and a practicable way to construct integrable couplings is further proposed. An application of the resulting general theory to the generalized Toda spectral problem yields two classes of integrable couplings for the generalized Toda hierarchy of lattice equations. The construction of integrable couplings using semidirect sums of Lie algebras provides a good source of information on complete classification of integrable lattice equations. [ABSTRACT FROM AUTHOR]

The Euclidean algebra e(2) is the Lie algebra of the group E(2) of Euclidean transformations of the plane. This paper examines finite dimensional representations of e(2) having two generators. To each representation with two generators we associate a graph. In term of graphs, we give a criterion for the indecomposability of such representations and describe an invariant for indecomposable representations. We also classify the indecomposable representations of dimensions 5 and 6, regardless of the number of generators (dimensions less than 5 have been classified). In each case there are finitely many such representations. Next, we show that for each dimension >=8 there are infinitely many nonequivalent indecomposable representations. [ABSTRACT FROM AUTHOR]

Let H=-∂x2+V(x) be a properly defined Schrödinger operator on L2(R) with real potentials of the form V(x)=q(x)+p′(x) (the derivative is understood in the distributional sense) with some p,q∈L2(R). We prove that the absolutely continuous spectrum of H fills (0,∞) which was previously proven by Deift-Killip for V∈L2(R). We also refine the 3/2-Lieb-Thirring inequality. [ABSTRACT FROM AUTHOR]

Generalized quantum statistics such as para-statistics is usually characterized by certain triple relations. In the case of para-Fermi statistics these relations can be associated with the orthogonal Lie algebra Bn=so(2n+1); in the case of para-Bose statistics they are associated with the Lie superalgebra B(0|n)=osp(1|2n). In a previous paper, a mathematical definition of “a generalized quantum statistics associated with a classical Lie algebra G” was given, and a complete classification was obtained. Here, we consider the definition of “a generalized quantum statistics associated with a basic classical Lie superalgebra G.” Just as in the Lie algebra case, this definition is closely related to a certain Z-grading of G. We give in this paper a complete classification of all generalized quantum statistics associated with the basic classical Lie superalgebras A(m|n),B(m|n),C(n), and D(m|n). [ABSTRACT FROM AUTHOR]

We give sufficient conditions for ergodicity of the Markovian semigroups associated to Dirichlet forms on standard forms of von Neumann algebras constructed by the method proposed by Park. We apply our result to show that the diffusion type Markovian semigroups for quantum spin systems are ergodic in the region of high temperatures where the uniqueness of the KMS state holds. [ABSTRACT FROM AUTHOR]

Fermions are expressed by polynomials of canonical generators of the Cuntz algebra O2 and they generate the U(1)-fixed point subalgebra A≡O2U(1) of O2 by the canonical gauge action. We extend the Fock and the infinite wedge representations of A to permutative representations of O2. By these extensions, the boson-fermion correspondence is rewritten by canonical generators of O2. [ABSTRACT FROM AUTHOR]

We present an extended version of max-plus algebra which includes the inverse operator of “max.” This algebra enables us to ultradiscretize the system including subtractions and obtain new ultradiscrete equations. The known ultradiscrete equations can also be recovered by this construction. [ABSTRACT FROM AUTHOR]

A basis of N2 projectors, each an N2×N2 matrix with constant elements, is implemented to construct a class of braid matrices R⁁(θ), θ being the spectral parameter. Only odd values of N are considered here. Our ansatz for the projectors Pα appearing in the spectral decomposition of R⁁(θ) leads to exponentials exp(mαθ) as the coefficient of Pα. The sums and differences of such exponentials on the diagonal and the antidiagonal, respectively, provide the (2N2-1) nonzero elements of R⁁(θ). One element at the center is normalized to unity. A class of supplementary constraints imposed by the braid equation leaves 1/2(N+3)(N-1) free parameters mα. The diagonalizer of R⁁(θ) is presented for all N. Transfer matrices t(θ) and L(θ) operators corresponding to our R⁁(θ) are studied. Our diagonalizer signals specific combinations of the components of the operators that lead to a quadratic algebra of N2 constant N×N matrices. The θ dependence factors out for such combinations. R⁁(θ) is developed in a power series in θ. The basic difference arising for even dimensions is made explicit. Some special features of our R⁁(θ) are discussed in a concluding section. [ABSTRACT FROM AUTHOR]

We establish the exact solution of the nonlinear Schrödinger equation with a delta-function impurity, representing a pointlike defect which reflects and transmits. We solve the problem both at the classical and the second quantized levels. In the quantum case the Zamolodchikov–Faddeev algebra, familiar from the case without impurities, is substituted by the recently discovered reflection-transmission (RT) algebra, which captures both particle–particle and particle–impurity interactions. The off-shell quantum solution is expressed in terms of the generators of the RT algebra and the exact scattering matrix of the theory is derived. [ABSTRACT FROM AUTHOR]

We extend the higher dimensional positive mass theorem in [Dai, X., Commun. Math. Phys. 244, 335–345 (2004)] to the Lorentzian setting. This includes the original higher dimensional positive energy theorem whose spinor proof is given in [Witten, E., Commun. Math. Phys. 80, 381–402 (1981)] and [Parker, T., and Taubes, C., Commun. Math. Phys. 84, 223–238 (1982)] for dimension 4 and in [Zhang, X., J. Math. Phys. 40, 3540–3552 (1999)] for dimension 5. [ABSTRACT FROM AUTHOR]

We derive several partial fractions expansions for products of Bessel functions, and use them to prove algebraic relationships between infinite series involving squares of Bessel functions. We also give formulas for the Taylor series coefficients of the zeros of Bessel functions, when the zeros are regarded as functions of the order x of Jx(y). [ABSTRACT FROM AUTHOR]

Starting from vector fields that preserve a differential form on a Riemann sphere with Grassmann variables, one can construct a superconformal algebra by considering central extensions of the algebra of vector fields. In this paper, the N=4 case is analyzed closely, where the presence of weight zero operators in the field theory forces the introduction of noncentral extensions. How this modifies the existing field theory, representation theory, and Gelfand–Fuchs constructions is discussed. It is also discussed how graded Riemann sphere geometry can be used to give a geometrical description of the central charge in the N=1 theory. [ABSTRACT FROM AUTHOR]

We devise a new simple loop algebra GM and an isospectral problem. By making use of the Tu scheme, the multicomponent generalized Kaup–Newell hierarchy is obtained. Furthermore, an expanding loop algebra FM of the loop algebra GM is presented. Based on FM, the multicomponent integrable couplings system with two arbitrary functions of the multicomponent generalized Kaup–Newell hierarchy are worked out. The method can be applied to other nonlinear evolution equations hierarchy. [ABSTRACT FROM AUTHOR]

In this paper we consider the Schrödinger equation with constant magnetic field of strength b>0 in all dimension. We study the behavior of the scattering amplitude and the scattering phase when the parameter b goes to infinity and the energy is far from the Landau levels. [ABSTRACT FROM AUTHOR]

We investigate the asymptotics of Hankel determinants of the form dctj,k=0N-1[∫ΩdxωN(X)¦¦i=1m¦μi-X¦2qiXj+k] as N → ∞ with q and μ fixed, where Ω is an infinite suhinterval of R and ωN(x) is a positive weight on Ω. Such objects are natural analogs of Tocplitz determinants generated by Fisher-Hartwig symbols, and arise in random matrix theory in the investigation of certain expectations involving random characteristic polynomials. The reduced density matrices of certain one- dimensional systems of trapped impenetrable bosons can also be expressed in terms of Hankel determinants of this form. We focus on the specific cases of scaled Hermite and Laguerre weights. We compute the asymptotics by using a duality formula expressing the N× N Hankel determinant as a 2(q1 +···+ qm)-fold integral, which is valid when each qi is natural. We thus verify, for such q, a recent conjecture of Forrester and Frankel derived using a log-gas argument. [ABSTRACT FROM AUTHOR]

The integrability of the deformed quantum elliptic Calogero–Moser problem introduced by Chalykh, Feigin, and Veselov is proven. Explicit recursive formulas for the integrals are found. For integer values of the parameter this implies the algebraic integrability of the systems. [ABSTRACT FROM AUTHOR]

We present and investigate a new class of quantum channels, what we call “universal collective rotation channels,” that includes the class of collective rotation channels as a special case. The fixed point set and noise commutant coincide for a channel in this class. Computing the precise structure of this C*-algebra is a core problem in a particular noiseless subsystem method of quantum error correction. We prove that there is an abundance of noiseless subsystems for every channel in this class and that the Young tableaux combinatorial machine may be used to explicitly compute these subsystems. [ABSTRACT FROM AUTHOR]

In this paper, local and nonlocal symmetry classifications are considered for four equivalent nonlinear telegraph equations. A complete potential symmetry classification of a scalar nonlinear telegraph equation is given through the point symmetry classification of a related potential system. Six new classes of equations are shown to admit potential symmetries. The relationships between local (including contact) and nonlocal (potential) symmetries of these equations are explored. A physical example is considered for possible applications of the obtained potential symmetries. [ABSTRACT FROM AUTHOR]

We identify the hyperbolic Kac Moody algebras for which there exists a Lagrangian of gravity, dilatons, and p-forms which produces a billiard that can be identified with their fundamental Weyl chamber. Because of the invariance of the billiard upon toroidal dimensional reduction, the list of admissible algebras is determined by the existence of a Lagrangian in three space–time dimensions, where a systematic analysis can be carried out since only zero-forms are involved. We provide all highest dimensional parent Lagrangians with their full spectrum of p-forms and dilaton couplings. We confirm, in particular, that for the rank 10 hyperbolic algebra, CE10=A15(2)∧, also known as the dual of B8∧∧, the maximally oxidized Lagrangian is nine-dimensional and involves besides gravity, 2 dilatons, a 2-form, a 1-form, and a 0-form. [ABSTRACT FROM AUTHOR]

A new geometrical framework for tetrad-affine formulation of gravity, pure or coupled with Yang–Mills fields, is proposed. After analyzing the geometrical properties of the new mathematical setting, field equations are deduced from a variational principle in the Poincaré–Cartan formalism. A generalized Noether Theorem is stated and classical relationship between symmetries and conserved quantities are recovered in the newer scheme. Some explicit examples are given. [ABSTRACT FROM AUTHOR]