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FINITE SEMIGROUPS ASSOCIATED WITH LINEAR ALGEBRAIC MONOIDS
The Quarterly Journal of Mathematics, 1986An analogue of the Bruhat decompositon is obtained for connected regular monoids with zero (a monoid is connected if it is a Zariski closed irreducible submonoid of the monoid of all matrices over an algebraically closed field).
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On certain algebras associated with finite groups
Ukrainian Mathematical Journal, 1992We construct new types of algebras which take into account the block structure of finite groups. We study the construction of such algebras. It is proved that the number of irreducible components of such an algebra is equal to the number of p blocks of the finite group whose defective groups contain a given p-element defined by the algebra.
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The Ext-algebra and associated monomial algebra of a finite dimensional K-algebra
Journal of Pure and Applied AlgebraLet \(K\) denote an algebraically closed field with characteristic 0, \(Q\) denote a finite quiver, (I) denote an admissible homogeneous ideal of the path algebra \(KQ\), \(A=KQ/I\) denote a graded finite dimensional \(K\)-algebra, and \(E(A)\) denote the Ext-algebra of \(A\).
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Moscow University Mathematics Bulletin, 2015
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, 2005
.In Section 1 we review various equivalent definitions of a vertex algebra V. The main novelty here is the definition in terms of an indefinite integral of the λ-bracket. In Section 2 we construct, in the most general framework, the Zhu algebra ZhuΓV, an
A. Sole, V. Kac
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.In Section 1 we review various equivalent definitions of a vertex algebra V. The main novelty here is the definition in terms of an indefinite integral of the λ-bracket. In Section 2 we construct, in the most general framework, the Zhu algebra ZhuΓV, an
A. Sole, V. Kac
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Identities in Vector Spaces Embedded in Finite Associative Algebras
Journal of Mathematical Sciences, 2017I. M. Isaev, A. V. Kislitsin
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Linear associative algebras with finitely many idempotents
Linear and Multilinear Algebra, 1996Let A be a linear (i.e., finite-dimensional) associative algebra with unity defined over K, an algebraically closed field. Then A with respect to its multiplication is an algebraic monoid over k, denoted by AM , and with respect to the the bracket forms a Lie algebra over K, denoted by AL .
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On the algebra associated with a finite hypergroupoid
1989The author investigates the algebra associated with a finite hypergroupoid. He studies the relations between quasi-hypergroups and division algebras. He finds some criteria for constructing hypergroupoids such that the associated algebra is associative. He introduces and studies a functor from the category of hypergroupoids to the category of algebras.
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Coxeter Transformations associated with Finite Dimensional Algebras
1999Let Λ be a finite dimensional algebra of finite global dimension. On the K-theoretic level the Auslander-Reiten translation on the bounded derived category of Λ-modules induces the Coxeter transformation which is an important invariant, preserved under derived equivalence, and displaying a lot of interesting homological information.
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