Abstract
For any complex parameters a and b, W(a, b) is the Lie algebra with basis {L i , W i | i ∈ ℤ} and relations [L i , L j ] = (j − i)L i +j, [L i , W j ] = (a + j + bi)W i+j , [W i , W j ] = 0. In this paper, indecomposable modules of the intermediate series overW(a, b) are classified. It is also proved that an irreducible Harish-Chandra W(a, b)-module is either a highest/lowest weight module or a uniformly bounded module. Furthermore, if a ∋ ℚ, an irreducible weight W(a, b)-module is simply a Vir-module with trivial actions of W k ’s.
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Su, Y., Xu, Y. & Yue, X. Indecomposable modules of the intermediate series over W(a, b). Sci. China Math. 57, 275–291 (2014). https://doi.org/10.1007/s11425-013-4630-0
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DOI: https://doi.org/10.1007/s11425-013-4630-0