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On solvable compact Clifford-Klein forms


Authors: Maciej Bocheński and Aleksy Tralle
Journal: Proc. Amer. Math. Soc. 145 (2017), 1819-1832
MSC (2010): Primary 57S30, 22F30, 22E40, 22E46
DOI: https://doi.org/10.1090/proc/13370
Published electronically: October 26, 2016
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Abstract: In this article we prove that under certain assumptions, a reductive homogeneous space $ G/H$ does not admit a solvable compact Clifford-Klein form. This generalizes the well known non-existence theorem of Benoist for nilpotent Clifford-Klein forms. This generalization works for a particular class of homogeneous spaces determined by ``very regular'' embeddings of $ H$ into $ G$.


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Additional Information

Maciej Bocheński
Affiliation: Department of Mathematics and Computer Science, University of Warmia and Mazury, Słoneczna 54, 10-710, Olsztyn, Poland
Email: mabo@matman.uwm.edu.pl

Aleksy Tralle
Affiliation: Department of Mathematics and Computer Science, University of Warmia and Mazury, Słoneczna 54, 10-710, Olsztyn, Poland
Email: tralle@matman.uwm.edu.pl

DOI: https://doi.org/10.1090/proc/13370
Keywords: Proper actions, homogeneous spaces, Lie groups
Received by editor(s): February 8, 2016
Received by editor(s) in revised form: June 22, 2016
Published electronically: October 26, 2016
Communicated by: Michael Wolf
Article copyright: © Copyright 2016 American Mathematical Society