On Some Lie Groups in Degenerate Clifford Geometric Algebras

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-07-18 DOI:10.1007/s00006-023-01290-y

Ekaterina Filimoshina, Dmitry Shirokov

引用次数: 0

Abstract

In this paper, we introduce and study five families of Lie groups in degenerate Clifford geometric algebras. These Lie groups preserve the even and odd subspaces and some other subspaces under the adjoint representation and the twisted adjoint representation. The considered Lie groups contain degenerate spin groups, Lipschitz groups, and Clifford groups as subgroups in the case of arbitrary dimension and signature. The considered Lie groups can be of interest for various applications in physics, engineering, and computer science.

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简并Clifford几何代数中的若干李群

本文介绍并研究了退化Clifford几何代数中的五个李群族。这些李群在伴随表示和扭曲伴随表示下保留了偶、奇子空间和其他一些子空间。在任意维数和特征的情况下，所考虑的李群包含退化的自旋群、Lipschitz群和Clifford群作为子群。所考虑的李群在物理、工程和计算机科学中的各种应用都可能引起兴趣。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.