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Simple weight modules over the $N=1$ Heisenberg–Virasoro superalgebra

Part of: Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  16 December 2024

Chao Lan  and
Dong Liu
Chao Lan
Affiliation:
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, Xinjiang, China e-mail: lanchao1027@163.com
Dong Liu*
Affiliation:
Department of Mathematics, Huzhou University, Zhejiang Huzhou, 313000, China
*
e-mail: liudong@zjhu.edu.cn
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Abstract

This paper presents a classification of all simple Harish-Chandra modules for the $N=1$ Heisenberg–Virasoro superalgebra, which turn out to be highest weight modules, lowest weight modules, and evaluation modules of the intermediate series (all weight spaces are one dimensional). Moreover, a characterization of the tensor product of highest weight modules with intermediate series modules is obtained.

Keywords

Heisenberg–Virasoro superalgebraHarish-Chandra moduleVerma moduletensor productintermediate series

MSC classification

Primary: 17B65: Infinite-dimensional Lie (super)algebras 17B68: Virasoro and related algebras 17B70: Graded Lie (super)algebras
Type
Article
Information
Canadian Mathematical Bulletin , Volume 68 , Issue 1 , March 2025 , pp. 198 - 212
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

This work was supported by the National Natural Science Foundation of China (Grant No. 12071405).

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