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Yang-Baxter equation and deformation of associative and Lie algebras

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

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References

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© 1992 Springer-Verlag

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Gurevich, D., Rubtsov, V. (1992). Yang-Baxter equation and deformation of associative and Lie algebras. In: Kulish, P.P. (eds) Quantum Groups. Lecture Notes in Mathematics, vol 1510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101177

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  • DOI: https://doi.org/10.1007/BFb0101177

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55305-2

  • Online ISBN: 978-3-540-47020-5

  • eBook Packages: Springer Book Archive