轴代数的中心扩展

IF 0.8 2区数学 Q2 MATHEMATICS Journal of Algebra Pub Date : 2024-09-05 DOI:10.1016/j.jalgebra.2024.09.001

Ivan Kaygorodov , Cándido Martín González , Pilar Páez-Guillán

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引用次数: 0

摘要

在本文中，我们进一步发展了斯基尔布雷德-桑德（Skjelbred-Sund）的方法，以构建轴向代数的中心扩展。我们用我们的方法证明了复简单有限维乔丹布拉的所有轴中心扩展（关于轴的最大集）都是分裂的，并且证明了在特征非 2 的代数闭域上维数 n≤4 的所有非分裂轴中心扩展都是乔丹的。此外，我们还给出了二维轴代数的分类，并描述了这些代数的一些重要性质。

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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Central extensions of axial algebras

In this article, we develop a further adaptation of the method of Skjelbred-Sund to construct central extensions of axial algebras. We use our method to prove that all axial central extensions (with respect to a maximal set of axes) of complex simple finite-dimensional Jordan algebras are split, and that all non-split axial central extensions of dimension $n \leq 4$ over an algebraically closed field of characteristic not 2 are Jordan. Also, we give a classification of 2-dimensional axial algebras and describe some important properties of these algebras.

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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.

期刊最新文献

Seminormal forms for the Temperley-Lieb algebra Editorial Board Characteristic subgroups and the R∞-property for virtual braid groups Central extensions of axial algebras Colocalizing subcategories of singularity categories