Quasifinite representations of a class of Block type Lie algebras B(q)
Quasifinite representations of a class of Block type Lie algebras B(q)
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DOI：
10.1016/j.jpaa.2011.10.012
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发表时间：
2011-02
影响因子：
0.8
通讯作者：
Yu-cai Su;Chunguang Xia;Ying Xu
中科院分区：
文献类型：
--
作者：
Yu-cai Su;Chunguang Xia;Ying Xu
Intrigued by a well-known theorem of Mathieu’s on Harish-Chandra modules over the Virasoro algebra, we show that any quasifinite irreducible module over a class of Block type Lie algebras B(q) is either a highest or lowest weight module, or else a uniformly bounded module, where the parameter q is a nonzero complex number. We also classify quasifinite irreducible highest weight B(q)-modules and irreducible B(q)-modules of the intermediate series. In particular, we obtain that an irreducible B(q)-module of the intermediate series may be a nontrivial extension of a V ir-module of the intermediate series if q is half of a negative integer, where V ir is a subalgebra of B(q) isomorphic to the Virasoro algebra.
