Leavitt Path Algebras in Which Every Lie Ideal is an Ideal and Applications

IF 0.4 3区数学 Q4 MATHEMATICS Transformation Groups Pub Date : 2024-02-16 DOI:10.1007/s00031-024-09848-1

Huỳnh Việt Khánh

引用次数: 0

Abstract

In this paper, we classify all Leavitt path algebras which have the property that every Lie ideal is an ideal. As an application, we show that Leavitt path algebras with this property provide a class of locally finite, infinite-dimensional Lie algebras whose locally solvable radical is completely determined. This particularly gives us a new class of semisimple Lie algebras over a field of prime characteristic.

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每个列理想都是理想的利维特路径代数及其应用

在本文中，我们对具有每个列理想都是理想这一性质的所有列维特路径代数进行了分类。作为应用，我们证明了具有这一性质的 Leavitt 路径代数提供了一类局部有限的无穷维李代数，其局部可解根完全确定。这尤其为我们提供了一类新的素特性域上的半简单李代数。

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

Transformation Groups 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

100

审稿时长

9 months

期刊介绍： Transformation Groups will only accept research articles containing new results, complete Proofs, and an abstract. Topics include: Lie groups and Lie algebras; Lie transformation groups and holomorphic transformation groups; Algebraic groups; Invariant theory; Geometry and topology of homogeneous spaces; Discrete subgroups of Lie groups; Quantum groups and enveloping algebras; Group aspects of conformal field theory; Kac-Moody groups and algebras; Lie supergroups and superalgebras.

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