Purely Hom-Lie bialgebras

• 来源期刊: 中国科学（数学）
• 年，卷（期）: 2018,（9）
• 页码范围: 1553-1566
• 页数: 14页
• 语种: 中文

摘要

In this paper,we first show that there is a Hom-Lie algebra structure on the set of (σ,σ)-derivations of an associative algebra.Then we construct the dual representation of a representation of a Hom-Lie algebra.We introduce the notions of a Manin triple for Hom-Lie algebras and a purely Hom-Lie bialgebra.Using the coadjoint representation,we show that there is a one-to-one correspondence between Manin triples for Hom-Lie algebras and purely Hom-Lie bialgebras.Finally,we study coboundary purely Hom-Lie bialgebras and construct solutions of the classical Hom-Yang-Baxter equations in some special Hom-Lie algebras using Hom-O-operators.