The fixed point set of the inverse involution on a Lie group
DOI:
https://doi.org/10.12775/TMNA.2022.012Keywords
Lie groups, symmetric spaces, fixed point theoryAbstract
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.References
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Copyright (c) 2023 Haibao Duan, Shali Liu
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