Irreducible Representations Of The Hom-Lie Algebra And Quasi-Hom-Lie Algebra

Hom-Lie algebra is a kind of generalized Lie algebra.It was proposed in the study of the deformations of Lie algebras,especially Witt algebra and Virasoro algebra.The structural theory of the Hom-Lie algebra has been fully studied,but the theoretical research on its representation is relatively little.This paper aims to study the representation theory of Hom-Lie algebra.Specifically,this paper mainly studies the irreducible representation of several classes of Lie algebras of Hom type,including the twisted Heisenberg-Virasoro algebra of Hom type,Virasoro algebra of Hom type and Virasoro algebra of Quasi-Hom type.Firstly,we induce the corresponding irreducible modules of Hom type from the irreducible Harish-Chandra modules over the twisted Heisenberg-Virasoro algebra.Secondly,we classify the intermediate series of indecomposable Harish-Chandra modules over Virasoro algebra of Hom type.Finally,we classify the intermediate series of indecomposable Harish-Chandra modules over Virasoro algebra of Quasi-Hom type.