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# Asian Journal of Mathematics

## Volume 18 (2014)

### Number 5

### Irreducible quasifinite modules over a class of Lie algebras of block type

Pages: 817 – 828

DOI: http://dx.doi.org/10.4310/AJM.2014.v18.n5.a3

#### Authors

#### Abstract

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.

#### Keywords

block type algebra, Virasoro algebra, quasifinite module

#### 2010 Mathematics Subject Classification

17B10, 17B20, 17B65, 17B66, 17B68