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March 2015 Realizations of globally exceptional $\mathbf{Z}_2 \times \mathbf{Z}_2$-symmetric spaces
Toshikazu Miyashita
Tsukuba J. Math. 38(2): 239-311 (March 2015). DOI: 10.21099/tkbjm/1429103724

Abstract

In [3], a classification is given of the exceptional $\mathbf{Z}_2 \times \mathbf{Z}_2$-symmetric spaces $G/K$, 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 $\mathbf{Z}_2 \times \mathbf{Z}_2$-symmetric spaces, globally.

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Toshikazu Miyashita. "Realizations of globally exceptional $\mathbf{Z}_2 \times \mathbf{Z}_2$-symmetric spaces." Tsukuba J. Math. 38 (2) 239 - 311, March 2015. https://doi.org/10.21099/tkbjm/1429103724

Information

Published: March 2015
First available in Project Euclid: 15 April 2015

zbMATH: 1315.53055
MathSciNet: MR3336271
Digital Object Identifier: 10.21099/tkbjm/1429103724

Subjects:
Primary: 17B40, 53C30, 53C35

Rights: Copyright © 2015 University of Tsukuba, Institute of Mathematics

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Vol.38 • No. 2 • March 2015
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