简并Clifford几何代数中的若干李群

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2023-07-18 DOI:10.1007/s00006-023-01290-y

Ekaterina Filimoshina, Dmitry Shirokov

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引用次数: 0

摘要

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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On Some Lie Groups in Degenerate Clifford Geometric Algebras

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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来源期刊

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.