Yang-Baxter equation and deformation of associative and Lie algebras

  • D. Gurevich
  • V. Rubtsov
I. Quantum Groups, Deformation Theory And Representation Theory
Part of the Lecture Notes in Mathematics book series (LNM, volume 1510)


We construct some cocycles (Hochschild and cyclic ones) connected with a classical R-matrix on associative and Lie algebras and “quantize” them. We treat “S-traces” (S is a solution of Yang-Baxter equation) on deformed algebras as a result of the quantization. The generalization of this construction is discussed.


Quantum Group Poisson Bracket Associative Algebra Tensor Category Associative Structure 
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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • D. Gurevich
    • 1
  • V. Rubtsov
    • 1
  1. 1.Moscow Branch of Center “Sophus Lie”USSR

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