Hom–Lie Algebras in Yetter–Drinfeld Categories.

In this paper, we introduce the definition of generalized H-Hom–Lie algebras (i.e., Hom-Lie algebras in the Yetter–Drinfeld category) for any Hopf algebra H, and obtain generalized H-Hom-Lie algebras from H-Hom-associative algebras (i.e., Hom-associative algebras in) and generalizedH-Lie algebras (i.e., Lie algebras in), respectively. We show that if A is a sum of two H-commutative Hom-associative subalgebras, then the H-commutator Hom-ideal of A is nilpotent. Finally, we describe the H-Hom-Lie ideal structures of the H-Hom-associative algebras by analogy with that of H-algebras. [ABSTRACT FROM AUTHOR]