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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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.

Article information

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

Dates
First available in Project Euclid: 2 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1417489243

Mathematical Reviews number (MathSciNet)
MR3287004

Zentralblatt MATH identifier
1361.17014

Subjects
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

Keywords
Block type algebra Virasoro algebra quasifinite module

Citation

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. https://projecteuclid.org/euclid.ajm/1417489243


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