Hom-Yang-Baxter equation, Hom-Lie algebras, and quasi-triangular bialgebras
Mathematical Physics
2009-03-27 v1 math.MP
Quantum Algebra
Rings and Algebras
Abstract
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.
Keywords
Cite
@article{arxiv.0903.0585,
title = {Hom-Yang-Baxter equation, Hom-Lie algebras, and quasi-triangular bialgebras},
author = {Donald Yau},
journal= {arXiv preprint arXiv:0903.0585},
year = {2009}
}
Comments
11 pages, to appear in Journal of Physics A