Non-virtually abelian discontinuous group actions vs. proper SL(2,R)-actions on homogeneous spaces

Aleksy Tralle; Maciej Bochenski; Piotr Jastrzebski; Willem A. de Graaf

Non-virtually abelian discontinuous group actions vs. proper SL(2,R)-actions on homogeneous spaces

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arxiv 2206.01069 v4 pith:W57CCFR3 submitted 2022-06-02 math.GR math.RT

Maciej Bochenski , Willem A. de Graaf , Piotr Jastrzebski , Aleksy Tralle This is my paper · ORCID

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keywords actionsgrouphomogeneousspacesabelianalgorithmsdiscontinuousnon-virtually

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We develop algorithms and computer programs which verify criteria of properness of discrete group actions on semisimple homogeneous spaces. We apply these algorithms to find new examples of non-virtually abelian discontinuous group actions on homogeneous spaces which do not admit proper SL(2,R)-actions.

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Exotic proper actions on homogeneous spaces via convex cocompact representations
math.GR 2025-01 accept novelty 8.0 of 10

There are reductive homogeneous spaces admitting proper actions of cocompact lattices of O(n,1) for n=2,3,4 while admitting no proper action of a non-compact semisimple subgroup.

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