Semisimple subalgebras in simple Lie algebras and a computational approach to the compact Clifford–Klein forms problem. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Bocheński, Maciej; Jastrzȩbski, Piotr; Szczepkowska, Anna; Tralle, Aleksy; Woike, Artur
• Is Part Of: Experimental mathematics. Volume 30:Issue 1(2021)
• Page Start: 86
• Page End: 94
• Publication Date: 2021-01-02
• Subjects: semisimple subalgebra -- Clifford–Klein form; 17B20 -- 22F30 -- 22E40 -- 65-05 -- 65F; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: 10.1080/10586458.2018.1492475
• Languages: English
• ISSNs: 1058-6458

Abstract

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.