The fixed point set of the inverse involution on a Lie group
| Autor: | Haibao Duan, Shali Liu |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Topological Methods in Nonlinear Analysis. :1-16 |
| ISSN: | 1230-3429 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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