李群上逆对合的不动点集

IF 0.7 4区数学 Q2 MATHEMATICS

Topological Methods in Nonlinear Analysis Pub Date : 2023-02-26 DOI:10.12775/tmna.2022.012

H. Duan, Shali Liu

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引用次数: 0

摘要

李群$G$上的逆对合是周期$2$变换$\gamma $，它将G$中的每个元素$G \发送到它的逆$G ^{-1}$。不动点集$\Fix(\gamma)$的变化对于李群$G$上的Morse函数的相关性和循环群$\mathbb{Z}_{2}$的$G$-表示具有重要意义。本文给出了一种计算简单李群不动点集$\Fix(\gamma)$的微分同态类型的方法。

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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The fixed point set of the inverse involution on a Lie group

The inverse involution on a Lie group $G$ is the periodic $2$ transformation $\gamma $ that sends each element $g\in G$ to its inverse $g^{-1}$. The variety of the fixed point set $\Fix(\gamma )$ is of importance for the relevances with Morse function on the Lie group $G$, and the $G$-representations of the cyclic group $\mathbb{Z}_{2}$. In this paper we develop an approach to calculate the diffeomorphism types of the fixed point sets $\Fix(\gamma)$ for the simple Lie groups.

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来源期刊

Topological Methods in Nonlinear Analysis 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Topological Methods in Nonlinear Analysis (TMNA) publishes research and survey papers on a wide range of nonlinear analysis, giving preference to those that employ topological methods. Papers in topology that are of interest in the treatment of nonlinear problems may also be included.