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arXiv · 1804.03484

Semisimple subalgebras in simple Lie algebras and a computational approach to the compact Clifford-Klein forms problem

Maciej Bocheński·Piotr Jastrzębski·Anna Szczepkowska·Aleksy Tralle·Artur Woike
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Abstract

In this paper we develop algorithms of finding homogeneous spaces of semisimple non-compact Lie groups which do not admit compact Clifford-Klein forms. We propose a computer program which checks if the given homogeneous space has a non-vanishing cohomological obstruction (found by Tholozan) to compact Clifford-Klein forms. By a numerical experiment we show that there is a large class of homogeneous spaces satisfying Tholozan's condition.

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Maciej Bocheński, Piotr Jastrzębski, Anna Szczepkowska, Aleksy Tralle, Artur Woike. 2018-04-10. Semisimple subalgebras in simple Lie algebras and a computational approach to the compact Clifford-Klein forms problem. https://doi.org/10.1080/10586458.2018.1492475

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