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

IF 1 3区数学 Q1 MATHEMATICS Forum Mathematicum Pub Date : 2024-06-25 DOI:10.1515/forum-2023-0320

Chunguang Xia, Tianyu Ma, Xiao Dong, Mingjing Zhang

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引用次数: 0

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.

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与维拉索罗代数有关的非无限级数列代数的表示

在本文中，我们研究了与维拉索罗代数有关的非无限分级列代数𝒲 ( ϵ ) {\mathcal{W}(\epsilon)} 的表示，其中ϵ = ± 1 {\epsilon=pm\ 1} 。准确地说，我们将自由的𝒰 ( 𝔥 ) {\mathcal{U}(\mathfrak{h})} 完全分类。 -𝒲 ( ϵ ) {\mathcal{W}(\epsilon)} 上的一阶模块，并发现这些模块结构与其他分级列的模块结构相当不同。我们还确定了这些模块的简单性和同构类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Forum Mathematicum 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.

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