The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
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DOI：
10.24330/ieja.266210
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发表时间：
2009-05
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影响因子：
--
通讯作者：
Donald Yau
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文献类型：
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作者：
Donald Yau
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.
