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

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Given an associative multiplication in matrix algebra compatible with the usual one or, in other words, linear deformation of 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.
26 pages, latex

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Quantum Algebra, Representation Theory, 17B80, 17B63, 32L81, 14H70

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http://salesiana.dossiersoluciones.com/handle/123456789/119172

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0611200
 http://arxiv.org/abs/math/0611200

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arXiv