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

2009/05/12 by Donald Yau, Yau, Donald · 3 citations
Mathematics · #16W30 #17A30 #17B37 #17B62 #81R50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0905.1890

openalex publication_date 2009/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Module Hom-algebras
• Quantum groups and representations of monoidal categories

Cited by

• ω-Lie bialgebras and ω-Yang-Baxter equation
• Paradigm of Nonassociative Hom-algebras and Hom-superalgebras
• Hom-alternative algebras and Hom-Jordan algebras

Related

• Hom-Yang-Baxter equations and Hom-Yang-Baxter systems
• Infinitesimal Hom-bialgebras and Hom-Lie bialgebras
• Local cocycle 3-Hom-Lie Bialgebras and 3-Lie Classical Hom-Yang-Baxter Equation
• The constructions of 3-Hom-Lie bialgebras
• sigma, tau-Rota-Baxter operators, infinitesimal Hom-bialgebras and the associative (Bi)Hom-Yang-Baxter equation