Classification of quasifinite representations of a Lie algebra related to Block type
Classification of quasifinite representations of a Lie algebra related to Block type
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DOI：
10.1016/j.jalgebra.2013.06.025
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发表时间：
2012-10
期刊：
影响因子：
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通讯作者：
Yu-cai Su;Chunguang Xia;Ying Xu
中科院分区：
文献类型：
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作者：
Yu-cai Su;Chunguang Xia;Ying Xu
MathieuʼS的一个著名定理指出，Virasoro代数上的Harish-Chandra模要么是最高权的模，要么是最低权的模，要么是中间级数的模。本文证明了与块型有关的李代数B的类似结果也适用于基为{Lα，i，C|α，i∈Z，i⩾0}和关系[Lα，i，Lβ，j]=((i+1)β−(j+1)α)Lα+β，i+j+δα+β，0δi+j，0α3−α12 C.即不可约拟有限B-模要么是最高权模，要么是最低权模，要么是中间级数模.
A well-known theorem of Mathieuʼs states that a Harish-Chandra module over the Virasoro algebra is either a highest weight module, a lowest weight module or a module of the intermediate series. It is proved in this paper that an analogous result also holds for the Lie algebra B related to Block type, with basis {L α, i, C| α, i∈ Z, i⩾ 0} and relations [L α, i, L β, j]=((i+ 1) β−(j+ 1) α) L α+ β, i+ j+ δ α+ β, 0 δ i+ j, 0 α 3− α 12 C. Namely, an irreducible quasifinite B-module is either a highest weight module, a lowest weight module or a module of the intermediate series.