The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras

Abstract

Motivated by recent work on Hom-Lie algebras and the Hom-Yang-Baxter equation, we introduce a twisted generalization of the classical Yang-Baxter equation (CYBE), called the classical Hom-Yang-Baxter equation (CHYBE). We show how an arbitrary solution of the CYBE induces multiple infinite families of solutions of the CHYBE. We also introduce the closely related structure of Hom-Lie bialgebras, which generalize Drinfel'd's Lie bialgebras. In particular, we study the questions of duality and cobracket perturbation and the sub-classes of coboundary and quasi-triangular Hom-Lie bialgebras.

22 pages

References in corpus (6)

• Hom-algebras and homology
• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
• Module Hom-algebras
• On unitality conditions for Hom-associative algebras
• On Hom type algebras
• Hom-Algebras and Hom-Coalgebras

Cited by in corpus (8)

• Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometry
• Paradigm of Nonassociative Hom-algebras and Hom-superalgebras
• Hom-alternative algebras and Hom-Jordan algebras
• Hom-Lie Superalgebras and Hom-Lie admissible Superalgebras
• Twisting Poisson algebras, coPoisson algebras and Quantization
• Infinitesimal Hom-bialgebras and Hom-Lie bialgebras
• Hom-power associative algebras
• Construtions and bimodules of BiHom-alternative and BiHom-Jordan algebras