Modules of the Intermediate Series over Not-finitely Graded Lie Algebras W(Γ).

Let W (Γ) be a class of not-finitely graded Lie algebras related to generalized Virasoro algebras with basis { L α , i , C   |   α ∈ Γ ,   i ∈ Z + } , which satisfies relations [ L α , i , L β , j ] = (β - α) L α + β , i + j + (j - i) L α + β , i + j + 1 + δ α + β , 0 δ i + j , 0 α 3 - α 12 C and [ C , L α , i ] = 0. In this paper, W (Γ) -modules of the intermediate series satisfying some conditions are constructed and classified. We also obtain modules of the intermediate series over the related Lie superalgebra. [ABSTRACT FROM AUTHOR]