Some modules over Lie algebras related to the Virasoro algebra

Abstract

In this paper, we study restricted modules over a class of (1/2)ℤ-graded Lie algebras 𝔤 related to the Virasoro algebra. We in fact give the classification of certain irreducible restricted 𝔤-modules in the sense of determining each irreducible restricted module up to an irreducible module over a subalgebra of 𝔤 which contains its positive part. Several characterizations of these irreducible 𝔤-modules are given. By the correspondence between restricted modules over 𝔤 and modules over the vertex algebra associated to 𝔤, we get the classification of certain irreducible modules over vertex algebras associated to these 𝔤.