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Quantum Groups pp 167-198 | Cite as

The Yang-Baxter Equation and (Co)Braided Bialgebras

  • Christian Kassel
Part of the Graduate Texts in Mathematics book series (GTM, volume 155)

Abstract

Part II is centered around the now famous Yang-Baxter equation whose so-lutions are the so-called R-matrices. We introduce the concept of braided bialgebras due to Drinfeld. These are bialgebras with a universal R-matrix inducing a solution of the Yang-Baxter equation on any of their mod-ules. This provides a systematic method to produce solutions of the Yang-Baxter equation. There is a dual notion of cobraided bialgebras. We show how to construct a cobraided bialgebra out of any solution of the Yang-Baxter equation by a method due to Faddeev, Reshetikhin and Takhtadjian [RTF89]. We conclude this chapter by proving that the quantum groups GLq(2) and SLq(2) of Chapter IV can be obtained by this method and that they are cobraided.

Keywords

Hopf Algebra Chapter VIII High Weight Vector Baxter Equation Cocommutative Hopf Algebra 
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 Science+Business Media New York 1995

Authors and Affiliations

  • Christian Kassel
    • 1
  1. 1.Institut de Recherche Mathématique AvancéeUniversité Louis Pasteur-C.N.R.S.StrasbourgFrance

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