Irreducible representations of the twisted Heisenberg-Virasoro algebra of Hom type

Abstract

Hom-Lie algebras are non-associative algebras generalizing Lie algebras by twisting the Jacobi identity by a linear map. In this paper, we mainly study the irreducible representation of the twisted Heisenberg-Virasoro algebra of Hom-type, which can be induced by the irreducible representations of its induced Lie algebra. In particular, we construct some kinds of irreducible representations of the twisted Heisenberg-Virasoro algebra of Hom-type.