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2007.191: Pairs of compatible associative algebras, classical Yang-Baxter and quiver representations

2007.191: Alexander Odesskii and Vladimir Sokolov (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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DOI: 10.1007/s00220-007-0361-9


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 2000 > 14 Algebraic geometry
MSC 2000 > 16 Associative rings and algebras
MSC 2000 > 17 Nonassociative rings and algebras
MIMS number:2007.191
Deposited By:Mrs Louise Healey
Deposited On:21 November 2007

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