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arXiv · 0905.1890

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

Donald Yau
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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.

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Donald Yau. 2009-05-12. The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras. https://arxiv.org/abs/0905.1890

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