Realizations of globally exceptional ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$- symmetric spaces

Abstract

A classification is given of the exceptional ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-symmetric spaces $G/K$ by A.Kollross, where $G$ is an exceptional compact Lie group or $Spin(8)$, and moreover the structure of $K$ is determined as Lie algebra. In the present article, we give a pair of commuting involutive automorphisms (involutions) $\tilde{\sigma },\tilde{\tau }$ of $G$ concretely and determine the structure of group $G^{\sigma }\cap G^{\tau }$ corresponding to Lie algebra ${\mathfrak{g}}^{\sigma }\cap {\mathfrak{g}}^{\tau }$, where $G$ is an exceptional compact Lie group. Thereby, we realize exceptional ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-symmetric spaces, globally.

48 pages

References in corpus (1)

• Exceptional Lie groups