Lie group concepts for S7 and its space of commuting elements

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-08-29 DOI:10.1016/j.topol.2025.109570

Jerry Wei

引用次数: 0

Abstract

The unit octonions,

S^{7}

, is an H-space which is not a Lie group due to failure of associativity. We examine the extent to which

S^{7}

has analogies of Lie group concepts such as maximal torus, Weyl group, Lie algebra, and exponential map. Moreover, we present a method for calculating the homology of the space of commuting n-tuples in

S^{7}

by induction on n.

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S7的李群概念及其交换元空间

单位八元数S7是一个h空间，由于不符合结合律而不是李群。我们研究了S7在多大程度上具有李群概念的相似性，如极大环面、Weyl群、李代数和指数映射。此外，我们还提出了一种利用n的归纳法计算S7中交换n元组空间的同调性的方法。

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

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.