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Tying up baric algebras
Baric algebra Indecomposable baric algebra Rings and Algebras
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2011/9/23
Abstract: Given two baric algebras $(A_1,\omega_1)$ and $(A_2,\omega_2)$ we describe a way to define a new baric algebra structure over the vector space $A_1\oplus A_2$, which we shall denote $(A_1\bo...
On embedding of dendriform algebras into Rota---Baxter algebras
dendriform algebras Rota Baxter algebras
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2011/9/29
Abstract: Following a recent work by C. Bai, O. Bellier, L. Guo, and X. Ni (arXiv:1106.6080) we define what is a dendriform di- or trialgebra in an arbitrary variety Var of algebras (associative, comm...
The Smooth Entropy Formalism on von Neumann Algebras
Smooth Entropy Formalism von Neumann Algebras Quantum Physics
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2011/10/9
Abstract: We discuss quantum information theoretical concepts on von Neumann algebras and lift the smooth entropy formalism to the most general quantum setting. For the smooth min- and max-entropies w...
Solvability of the $H^\infty$ algebraic Riccati equation in Banach algebras
Riccati equations Banach algebras Systems over rings H1 control Spatially distributed dynamical systems
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2011/9/21
Abstract: Let $R$ be a commutative complex unital semisimple Banach algebra with the involution $\cdot ^\star$. Sufficient conditions are given for the existence of a stabilizing solution to the $H^\i...
Topologies on Central Extensions of Von Neumann Algebras
Von Neumann Algebras Topologies Operator Algebras
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2011/9/21
Abstract: Given a von Neumann algebra $M$ we consider the central extension $E(M)$ of $M.$ We introduce the topology $t_c(M)$ on $E(M)$ generated by a center-valued norm and prove that it coincides wi...
Special biserial algebras with no outer derivations
Special biserial algebras Hochschild cohomology simple connectedness fundamental group
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2011/9/21
Abstract: Let $A$ be a special biserial algebra over an algebraically closed field. We show that the first Hohchshild cohomology group of $A$ with coefficients in the bimodule $A$ vanishes if and only...
Handsaw quiver varieties and finite W-algebras
Handsaw quiver varieties finite W-algebras Quantum Algebra
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2011/9/20
Abstract: Following Braverman-Finkelberg-Feigin-Rybnikov (arXiv:1008.3655), we study the convolution algebra of a handsaw quiver variety, a.k.a. a parabolic Laumon space, and a finite W-algebra of typ...
Sperner property and finite-dimensional Gorenstein algebras associated to matroids
Sperner property finite-dimensional Gorenstein algebras matroids Commutative Algebra
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2011/9/21
Abstract: We prove the Lefschetz property for a certain class of finite-dimensional Gorenstein algebras associated to matroids. Our result implies the Sperner property of the vector space lattice. We ...
Simple G-graded algebras and their polynomial identities
graded algebra polynomial identity
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2011/9/19
Abstract: Let G be any group and F an algebraically closed field of characteristic zero. We show that any two G-graded finite dimensional G-simple algebras over F are G-graded isomorphic if and only i...
Affine.m - Mathematica package for computations in representation theory of finite-dimensional and affine Lie algebras
Mathematica Lie algebra ane Lie algebra Kac-Moody algebra root system weights irreducible modules CFT Integrable systems
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2011/9/19
Abstract: In this paper we present Affine.m - program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. Algorithms are based ...
Calabi-Yau algebras viewed as deformations of Poisson algebras
Koszul algebras Calabi-Yau algebras Poisson algebras deformations of algebras Poisson homology Hochschild homology
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2011/9/19
Abstract: We define a family of 3-Calabi-Yau algebras by potentials. For some of these algebras, we explicitly compute the Hochschild homology with the help of Poisson homology. The point is that the ...
Ext algebra of Nichols algebras of type $A_2$
Nichols algebra Ext algebra Quantum Algebra
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2011/9/19
Abstract: We give the full structure of the Ext algebra of a Nichols algebra of type $A_2$ by using the Hochschild-Serre spectral sequence. As an application, we show that the pointed Hopf algebras $u...
δ-derivations of n-ary algebras
δ-derivation Filippov algebra ternary Malcev algebra
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2011/9/19
Abstract: We defined \delta-derivations of n-ary algebras. We described \delta-derivations of (n+1)-dimensional n-ary Filippov algebras and simple finite-dimensional Filippov algebras over algebraical...
Leibniz algebras on symplectic plane and cohomological vector fields
Leibniz algebras symplectic-Poisson geometry anti-cyclic operads Quantum Algebra
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2011/9/16
Abstract: By using help of algebraic operad theory, Leibniz algebra theory and symplectic-Poisson geometry are connected. We introduce the notion of cohomological vector field defined on nongraded sym...
On centralizer algebras for spin representations
centralizer algebras spin representations Quantum Algebra
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2011/9/16
Abstract: We give a presentation of the centralizer algebras for tensor products of spinor representations of quantum groups via generators and relations. In the even-dimensional case, this can be des...