Double Hom-Associative Algebra and Double Hom–Lie Bialgebra

Abstract

Recently, Hom-structures have been widely investigated in literature. In this paper, we introduce the conceptions of double Hom-associative algebras and double Hom–Lie bialgebras, and give a necessary and sufficient condition for double Hom-associative algebras to be Hom-associative algebras. Meanwhile, we characterize a classical Hom–Yang–Baxter equation in terms of both Hom–Lie algebra morphisms and Hom–Lie coalgebra morphisms. Last but not least, we introduce the notion of double Hom–Lie bialgebras, and prove that double Hom-associative algebras are indeed quasi-triangular Hom–Lie bialgebras.