Solutions Of The Yang-baxter Equations From Braided-Lie Algebras And Braided Groups

Details Solutions Of The Yang-baxter Equations From Braided-Lie Algebras And Braided Groups Solutions Of The Yang-baxter Equations From Braided-Lie Algebras And Braided Groups

1993-12-15

arxiv.org/abs/hep-th/9312140v2

J.Knot Theor.Ramifications 4 (1995) 673-697

Physics

High Energy Physics

High Energy Physics - Theory

29 pages

Scientific paper

We obtain an R-matrix or matrix representation of the Artin braid group acting in a canonical way on the vector space of every (super)-Lie algebra or braided-Lie algebra. The same result applies for every (super)-Hopf algebra or braided-Hopf algebra. We recover some known representations such as those associated to racks. We also obtain new representations such as a non-trivial one on the ring $k[x]$ of polynomials in one variable, regarded as a braided-line. Representations of the extended Artin braid group for braids in the complement of $S^1$ are also obtained by the same method.

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