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HARISH-CHANDRA MODULES OVER THE ℚ HEISENBERG–VIRASORO ALGEBRA

Part of: Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  10 August 2010

XIANGQIAN GUO ,
XUEWEN LIU  and
KAIMING ZHAO
XIANGQIAN GUO*
Affiliation:
Department of Mathematics, Zhengzhou University, Zhengzhou 450001, Henan, PR China (email: guoxq@zzu.edu.cn)
XUEWEN LIU
Affiliation:
Department of Mathematics, Zhengzhou University, Zhengzhou 450001, Henan, PR China (email: liuxw@zzu.edu.cn)
KAIMING ZHAO
Affiliation:
Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada N2L 3C5 Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, PR China (email: kzhao@wlu.ca)
*
✉For correspondence; e-mail: guoxq@zzu.edu.cn
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Abstract

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In this paper, it is proved that all irreducible Harish-Chandra modules over the ℚ Heisenberg–Virasoro algebra are of the intermediate series (all weight spaces are at most one-dimensional).

Keywords

Virasoro algebraℚ Heisenberg–Virasoro algebramodules of the intermediate series

MSC classification

Secondary: 17B10: Representations, algebraic theory (weights) 17B68: Virasoro and related algebras 17B70: Graded Lie (super)algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 89 , Issue 1 , August 2010 , pp. 9 - 15
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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