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 |
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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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