Abstract
For any module V over the two-dimensional non-abelian Lie algebra b and scalar α ∈ C, we define a class of weight modules F α(V) with zero central charge over the affine Lie algebra A (1)1 . These weight modules have infinitedimensional weight spaces if and only if V is infinite dimensional. In this paper, we will determine necessary and sufficient conditions for these modules F α(V) to be irreducible. In this way, we obtain a lot of irreducible weight A (1)1 -modules with infinite-dimensional weight spaces.
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Liu, G., Zhao, Y. Irreducible A (1)1 -modules from modules over two-dimensional non-abelian Lie algebra. Front. Math. China 11, 353–363 (2016). https://doi.org/10.1007/s11464-016-0503-5
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DOI: https://doi.org/10.1007/s11464-016-0503-5