Various Characteristic Properties of Lipschitzian Elements in Clifford Algebras

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-07-12 DOI:10.1007/s00006-023-01288-6

Jacques Helmstetter

引用次数: 1

Abstract

In most cases, the Lipschitz monoid \(\textrm{Lip}(V,Q)\) is the multiplicative monoid (or semi-group) generated in the Clifford algebra \(\textrm{Cl}(V,Q)\) by the vectors of V. But the elements of \(\textrm{Lip}(V,Q)\) satisfy many other characteristic properties, very different from one another, which may as well be used as definitions of \(\textrm{Lip}(V,Q)\). The present work proposes several characteristic properties, and explores some of the ways that enable us to link one property to another.

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Clifford代数中Lipschitzian元素的各种特征性质

在大多数情况下，Lipschitz monoid \（\textrm｛Lip｝（V，Q）\）是Clifford代数\（\txtrm｛Cl｝（V，Q））中由V的向量生成的乘法monoid（或半群）。本工作提出了几个特性，并探索了一些使我们能够将一个特性与另一个特性联系起来的方法。

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.