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

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

2006-11-07

arxiv.org/abs/math/0611200v1

Mathematics

Quantum Algebra

26 pages, latex

Scientific paper

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.

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