Abstract
The compact simply connected Riemannian -symmetric spaces were classified by J. A. Jiménez according to type of the Lie algebras. As homogeneous manifolds, these spaces are of the form , where is a connected compact simple Lie group with an automorphism of order four on and is a fixed points subgroup of . According to the classification by J. A. Jiménez, there exist seven compact simply connected Riemannian -symmetric spaces in the case where is of type . In the present article, we give the explicit form of automorphisms , and of order four on induced by the -linear transformations , and of the 248-dimensional -vector space , respectively. Further, we determine the structure of these fixed points subgroups , and of . These amount to the global realizations of three spaces among seven Riemannian 4-symmetric spaces above corresponding to the Lie algebras , and , where . With this article, the all realizations of inner automorphisms of order four and fixed points subgroups by them have been completed in .
Citation
Toshikazu Miyashita. "Realizations of inner automorphisms of order four and fixed points subgroups by them on the connected compact exceptional Lie group , Part III." Tsukuba J. Math. 46 (1) 39 - 65, July 2022. https://doi.org/10.21099/tkbjm/20224601039
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