THE CLASSICAL HOM-YANG-BAXTER EQUATION AND HOM-LIE BIALGEBRAS

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International Electronic Journal of Algebra
Volume:17 Issue:17
THE CLASSICAL HOM-YANG-BAXTER EQUATION AND HOM-LIE BIALGEBRAS

THE CLASSICAL HOM-YANG-BAXTER EQUATION AND HOM-LIE BIALGEBRAS

Pages : 11-45

View : 37 | Download : 14

Publication Date : 2015-06-01

Article Type : Research Paper

Abstract :Motivated by recent work on Hom-Lie algebras and the HomYang-Baxter equation, we introduce a twisted generalization of the classical Yang-Baxter equation insert ignore into journalissuearticles values(CYBE);, called the classical Hom-Yang-Baxter equation insert ignore into journalissuearticles values(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.
Keywords : The classical Hom Yang Baxter equation, Hom Lie bialgebra

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