Homogeneous spaces of real simple Lie groups with proper actions of non virtually abelian discrete subgroups: a calculational approach

Let G be a simple non-compact linear connected Lie group and H 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 of G. We develop an algorithm for finding such homogeneous s...

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Bibliographic Details
Published in:arXiv.org 2021-06
Main Authors: Bochenski, Maciej, Jastrzebski, Piotr, Tralle, Aleksy
Format: Article
Language:English
Subjects:
Algorithms
Lie groups
Subgroups
Online Access:Get full text
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Summary:Let G be a simple non-compact linear connected Lie group and H 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 of 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 of G in the case when G has rank at most 8, and H is a maximal proper semisimple subgroup.
ISSN:2331-8422
DOI:10.48550/arxiv.2106.05777