The Yang-Baxter Equation and (Co)Braided Bialgebras
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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.
KeywordsHopf Algebra Chapter VIII High Weight Vector Baxter Equation Cocommutative Hopf Algebra
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