The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
arXiv:0905.1890
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.
arXiv comment22 pages
References in corpus (7)
Cited by in corpus (19)
- Hom-bialgebras and comodule Hom-algebras
- Hom-quantum groups I: quasi-triangular Hom-bialgebras
- On n-ary Hom-Nambu and Hom-Nambu-Lie algebras
- Yetter-Drinfeld modules for Hom-bialgebras
- Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometry
- Hom-quantum groups III: Representations and module Hom-algebras
- Paradigm of Nonassociative Hom-algebras and Hom-superalgebras
- Hom-Maltsev, Hom-alternative, and Hom-Jordan algebras
- 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
- Free involutive Hom-semigroups and Hom-associative algebras
- On n-ary Hom-Nambu and Hom-Maltsev algebras
- Universal enveloping algebras and Poincaré-Birkhoff-Witt theorem for involutive Hom-Lie algebras
- Hom-power associative algebras
- Construtions and bimodules of BiHom-alternative and BiHom-Jordan algebras
- On hom-Lie algebras
- A new approach to hom-Lie bialgebras