Irreducible quasifinite modules over a class of Lie algebras of Block type. (English) Zbl 1361.17014

Chen, Hongjia; Guo, Xiangqian; Zhao, Kaiming

Asian J. Math. 18, No. 5, 817-828 (2014).

Summary: For any nonzero complex number \(q\), there is a Lie algebra of Block type, denoted by \(\mathcal{B}(q)\). In this paper, a complete classification of irreducible quasifinite modules is given. More precisely, an irreducible quasifinite module is a highest weight or lowest weight module, or a module of intermediate series. As a consequence, a classification for uniformly bounded modules over another class of Lie algebras, the semi-direct product of the Virasoro algebra and a module of intermediate series, is also obtained. Our method is conceptional, instead of computational.

MSC:

17B10	Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B65	Infinite-dimensional Lie (super)algebras
17B68	Virasoro and related algebras

Keywords:

Block type algebra; Virasoro algebra; quasifinite module