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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)

Abstract

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.

Keywords

Quantum Group Poisson Bracket Associative Algebra Tensor Category Associative Structure 
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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References

  1. [D]
    Drinfeld V., On constant, quasiclassical solutions of the Yang-Baxter quantum equation, Sov. Math., Dokl. 28 (1983), 667–671.MathSciNetzbMATHGoogle Scholar
  2. [G1]
    Gurevich D., The Yang-Baxter equation and generalization of formal Lie theory, Sov. Math., Dokl. 33 (1986), 758–762.CrossRefzbMATHGoogle Scholar
  3. [G2]
    Gurevich D., Equation de Yang-Baxter et quantification des cocycles, Compt. Rend. Ac. Sci. Paris, Ser. 1 310 (1990), 845–848.MathSciNetzbMATHGoogle Scholar
  4. [G3]
    Gurevich D., Algebraic aspects of the quantum Yang-Baxter equation, Algebra Anal 2 no. 4 (1990), 119–148. (in Russian)MathSciNetzbMATHGoogle Scholar
  5. [GRZ]
    Gurevich D., Rubtsov V., Zobin N., Quantization of Poisson pairs: the R-matrix approach, Geometry and Physics (to appear).Google Scholar
  6. [L]
    Lyubashenko V., Vectorsymmetries, Rep. Dep. Math., Univ. of Stockholm 19 (1987), 1–77.Google Scholar

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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