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Original Articles

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

, , , &
Pages 86-94 | Published online: 08 Jan 2019
 

Abstract

In this article, we develop the algorithm for 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.

MATHEMATICS SUBJECT CLASSIFICATION:

Acknowledgments

We thank Willem de Graaf for his help in getting some literature sources.

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