Representations of non-finitely graded Lie algebras related to Virasoro algebra-Reference-Cited by-同舟云学术

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

Published:2024-06-26 Issue: Volume: Page:
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Xia Chunguang¹^ORCID,Ma Tianyu²,Dong Xiao²,Zhang Mingjing²^ORCID

Affiliation:

1. School of Mathematics , 12392 China University of Mining and Technology , Xuzhou 221116; and School of Mathematical Sciences, Xiamen University, Xiamen 361005 , P. R. China

2. School of Mathematics , 12392 China University of Mining and Technology , Xuzhou 221116 , P. R. China

Abstract

Abstract In this paper, we study representations of non-finitely graded Lie algebras 𝒲 ⁢ ( ϵ )

{\mathcal{W}(\epsilon)}

related to Virasoro algebra, where ϵ = ± 1

{\epsilon=\pm 1}

. Precisely speaking, we completely classify the free 𝒰 ⁢ ( 𝔥 )

{\mathcal{U}(\mathfrak{h})}

-modules of rank one over 𝒲 ⁢ ( ϵ )

{\mathcal{W}(\epsilon)}

, 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.

Funder

Fundamental Research Funds for the Central Universities

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/forum-2023-0320/pdf

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