每个列理想都是理想的利维特路径代数及其应用

Pub Date : 2024-02-16 DOI:10.1007/s00031-024-09848-1

Huỳnh Việt Khánh

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引用次数: 0

摘要

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

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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