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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...
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...
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...
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...
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...
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...
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...
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 ...
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...
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 ...
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 ...
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...
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...
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...
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...

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