Pairs of compatible associative algebras, classical Yang-Baxter and quiver representations

Odesskii, Alexander and Sokolov, Vladimir (2007) Pairs of compatible associative algebras, classical Yang-Baxter and quiver representations. Communications in Mathematical Physics. pp. 1-17. ISSN 1432-0916

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Abstract

Given an associative multiplication in matrix algebra compatible with the usual one or, in other words, a linear deformation of the matrix algebra, we construct a solution to the classical Yang-Baxter equation. We also develop a theory of such deformations and construct numerous examples. It turns out that these deformations are in one-to-one correspondence with representations of certain algebraic structures, which we call M-structures. We also describe an important class of M-structures related to the affine Dynkin diagrams of A, D, E-type. These M-structures and their representations are described in terms of quiver representations.

Item Type:	Article
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 14 Algebraic geometry MSC 2010, the AMS's Mathematics Subject Classification > 16 Associative rings and algebras MSC 2010, the AMS's Mathematics Subject Classification > 17 Nonassociative rings and algebras
Depositing User:	Ms Lucy van Russelt
Date Deposited:	21 Nov 2007
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/935

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