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.
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Odesskii, A., Sokolov, V. Pairs of Compatible Associative Algebras, Classical Yang-Baxter Equation and Quiver Representations. Commun. Math. Phys. 278, 83–99 (2008). https://doi.org/10.1007/s00220-007-0361-9
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DOI: https://doi.org/10.1007/s00220-007-0361-9