Asian Journal of Mathematics

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

Hongjia Chen, Xiangqian Guo, and Kaiming Zhao

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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.

Article information

Asian J. Math., Volume 18, Number 5 (2014), 817-828.

First available in Project Euclid: 2 December 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 17B10: Representations, algebraic theory (weights) 17B20: Simple, semisimple, reductive (super)algebras 17B65: Infinite-dimensional Lie (super)algebras [See also 22E65] 17B66: Lie algebras of vector fields and related (super) algebras 17B68: Virasoro and related algebras

Block type algebra Virasoro algebra quasifinite module


Chen, Hongjia; Guo, Xiangqian; Zhao, Kaiming. Irreducible quasifinite modules over a class of Lie algebras of block type. Asian J. Math. 18 (2014), no. 5, 817--828.

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