Representations of non-finitely graded Lie algebras related to Virasoro algebra

Abstract In this paper, we study representations of non-finitely graded Lie algebras 𝒲 ⁢ (ϵ) W () related to Virasoro algebra, where ϵ = ± 1 = 1. Precisely speaking, we completely classify the free 𝒰 ⁢ (𝔥) U (h) -modules of rank one over 𝒲 ⁢ (ϵ) W (), and find that these module structures are rather different from those of other graded Lie algebras. We also determine the simplicity and isomorphism classes of these modules.