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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

  • Alexander OdesskiiEmail author
  • Vladimir Sokolov
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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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