Hom-ideal structure of monoidal Hom-algebras in a category

Abstract

In this paper, firstly we study the central invariant ZH(L)0 of generalized Hom-Lie algebras L, which are monoidal Hom-Lie algebras in the category [Formula: see text] of H-modules for a triangular Hopf algebra (H, R). If V is an H-Hom-Lie ideal of [L, L], under certain conditions we obtain V0 ⊆ ZH(L)0, where V0 is the monoidal Hom-subalgebra of H-invariant of V. Secondly, we describe the H-Hom-Lie ideal structure of monoidal Hom-algebras in a module category.