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Representations of non-finitely graded Lie algebras related to Virasoro algebra

  • Chunguang Xia ORCID logo EMAIL logo , Tianyu Ma , Xiao Dong and Mingjing Zhang ORCID logo
Published/Copyright: June 26, 2024

Abstract

In this paper, we study representations of non-finitely graded Lie algebras 𝒲 ( ϵ ) related to Virasoro algebra, where ϵ = ± 1 . Precisely speaking, we completely classify the free 𝒰 ( 𝔥 ) -modules of rank one over 𝒲 ( ϵ ) , and find that these module structures are rather different from those of other graded Lie algebras. We also determine the simplicity and isomorphism classes of these modules.

MSC 2020: 17B10; 17B65; 17B68

Communicated by Jan Frahm


Award Identifier / Grant number: 2019QNA34

Funding statement: This work was supported by the Fundamental Research Funds for the Central Universities (No. 2019QNA34).

Acknowledgements

We are very grateful to the referee for helpful comments that have improved the manuscript. We also thank Professor Y. Su for helpful discussions.

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Received: 2023-09-04
Revised: 2024-05-22
Published Online: 2024-06-26
Published in Print: 2025-02-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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