Homogeneous spaces of real simple Lie groups with proper actions of non virtually abelian discrete subgroups: A computational approach. (November 2022)

• Record Type: Journal Article
• Authors: Bocheński, Maciej; Jastrzȩbski, Piotr; Tralle, Aleksy
• Is Part Of: Journal of symbolic computation. Volume 113(2022)
• Page Start: 171
• Page End: 180
• Publication Date: 2022-11
• Subjects: 17B20 -- 20-04 -- 20G20 -- 22F30 -- 22E40 -- 65-05 -- 65F; Proper actions -- Semisimple algebras -- Clifford-Klein forms; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2022.04.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Let G be a simple non-compact linear connected Lie group and H ⊂ G be a closed non-compact semisimple subgroup. We are interested in finding classes of homogeneous spaces G / H admitting proper actions of discrete non-virtually abelian subgroups Γ ⊂ G . We develop an algorithm for finding such homogeneous spaces. As a testing example we obtain a list of all non-compact homogeneous spaces G / H admitting proper action of a discrete and non virtually abelian subgroup Γ ⊂ G in the case when G has rank at most 8, and H is a maximal proper semisimple subgroup, provided that the pair ( g, h ) is contained in a database created by De Graaf and Marrani.