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

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.

arXiv comment11 pages, to appear in Journal of Physics A

References in corpus (1)

• Deformations of Lie Algebras using $\sigma$-derivations

Cited by in corpus (10)

• Representations of hom-Lie algebras
• Hom-Lie 2-algebras
• On n-ary Hom-Nambu and Hom-Nambu-Lie algebras
• Yetter-Drinfeld modules for Hom-bialgebras
• Hom-Novikov algebras
• Purely Hom-Lie bialgebras
• Hom Gel'fand-Dorfman bialgebras and Hom-Lie conformal algebras
• Second Cohomology of q-deformed Witt superalgebras
• Relative Hom-Hopf modules and total integrals
• $f$-Racks, $f$-Quandles, their Extensions and Cohomology