Homogeneous spaces of real simple Lie groups with proper actions of non virtually abelian discrete subgroups: A computational approach. (November 2022) - Bocheński, Maciej; Jastrzȩbski, Piotr; Tralle, Aleksy
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.