Hom-Yang-Baxter equation, Hom-Lie algebras, and quasi-triangular bialgebras

Details Hom-Yang-Baxter equation, Hom-Lie algebras, and quasi-triangular bialgebras Hom-Yang-Baxter equation, Hom-Lie algebras, and quasi-triangular bialgebras

2009-03-03

arxiv.org/abs/0903.0585v1

J.Phys.A42:165202,2009

Physics

Mathematical Physics

11 pages, to appear in Journal of Physics A

Scientific paper

10.1088/1751-8113/42/16/165202

We study a twisted version of the Yang-Baxter Equation, called the Hom-Yang-Baxter Equation (HYBE), which is motivated by Hom-Lie algebras. Three classes of solutions of the HYBE are constructed, one from Hom-Lie algebras and the others from Drinfeld's (dual) quasi-triangular bialgebras. Each solution of the HYBE can be extended to operators that satisfy the braid relations. Assuming an invertibility condition, these operators give a representation of the braid group.

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