Non-weight modules over the Lie (super)algebras related to the Virasoro algebra

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-07-17 DOI:10.1016/j.jalgebra.2025.06.047

Yan-an Cai, Rencai Lü, Xinyue Wang

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引用次数: 0

Abstract

In this paper, we denote by

L

the infinite-dimensional Lie (super)algebra related to the Virasoro algebra introduced in [4]. We classify a class of non-weight modules over

L

and its universal central extension

\hat{L}

that are free of rank 1 when restricted to

U (h)

, where

h

is a toral subalgebra of

L

. We also determine both the simplicity and isomorphism classes of these modules. Furthermore, we consider the tensor products of finitely many rank 1 free simple modules with an arbitrary simple restricted module over

\hat{L}

. The simplicity and isomorphism classes are characterized. Finally, we apply our results to recover some known results and classify such non-weight modules over several new Lie (super)algebras.

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与Virasoro代数相关的Lie（超）代数上的非权模

本文用L表示与[4]中引入的Virasoro代数相关的无限维Lie（超）代数。我们在L上分类了一类非权模和它的普遍中心扩展L -，当被限制于U(h)时，它们的秩不为1，其中h是L的一个总子代数，我们还确定了这些模的简单性和同构性。进一步，我们考虑了有限多个秩1自由简单模与L -上任意简单受限模的张量积。该类具有简单性和同构性的特点。最后，我们应用我们的结果恢复了一些已知的结果，并在几个新的李（超）代数上对这些非权模进行了分类。

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

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.