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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.
Xia et al. (Tue,) studied this question.