Asian Journal of Mathematics

Volume 18 (2014)

Number 5

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

Pages: 817 – 828



Hongjia Chen (School of Mathematical Sciences, University of Science and Technology of China, Wu Wen Tsun Key Laboratory of Mathematics, Chinese Academy of Sciences, Hefei, Anhui, China)

Xiangqian Guo (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan, China)

Kaiming Zhao (Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada; and College of Mathematics and Information Science, Hebei Normal (Teachers) University, Shijiazhuang, Hebei, China)


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.


block type algebra, Virasoro algebra, quasifinite module

2010 Mathematics Subject Classification

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

Full Text (PDF format)