Communications in Mathematical Physics

, Volume 278, Issue 1, pp 83–99 | Cite as

Pairs of Compatible Associative Algebras, Classical Yang-Baxter Equation and Quiver Representations

Article

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.

Keywords

Meromorphic Function Associative Algebra Matrix Algebra Dynkin Diagram Quiver Representation 
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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsMoscowRussia
  2. 2.School of MathematicsThe University of ManchesterManchesterUK

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