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
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 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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