Nonexistence of standard compact Clifford–Klein forms of homogeneous spaces of exceptional Lie groups

Bocheński, Maciej; Jastrzȩbski, Piotr; Tralle, Aleksy

doi:10.1090/mcom/3493

Nonexistence of standard compact Clifford–Klein forms of homogeneous spaces of exceptional Lie groups
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by Maciej Bocheński, Piotr Jastrzȩbski and Aleksy Tralle HTML | PDF

Math. Comp. 89 (2020), 1487-1499 Request permission

Abstract:

We use a computer-aided approach to prove that there are no standard compact Clifford–Klein forms of homogeneous spaces of exceptional Lie groups. This yields further support for Kobayashi’s conjecture about possible compact Clifford–Klein forms. Our approach is based on the algorithms developed in this work. They are inspired by the algorithmic methods of classifying semisimple subalgebras in simple Lie algebras developed by Faccin and de Graaf. Also, we use the databases created by them. These algorithms eliminate the majority of possibilities. We complete the proof using Kobayashi’s criterion for properness of the Lie group action.

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