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Journal of Lie Theory 32 (2022), No. 3, 813--819
Copyright Heldermann Verlag 2022

On Semisimple Standard Compact Clifford-Klein Forms

Maciej Bochenski
Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Olsztyn, Poland

We give the classification of standard compact Clifford-Klein forms corresponding to triples (g, h, l) such that g = h + l and g is a sum of two absolutely simple ideals. The classification is done using Onishchik's results concerning semisimple decompositions of semisimple Lie algebras. Using this classification we obtain new examples of reductive homogeneous spaces admitting non-standard compact Clifford-Klein forms.

Keywords: Homogeneous spaces, proper actions, discrete subgroups, Clifford-Klein forms.

MSC: 57S30, 17B20, 22F30.

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