arXiv subjects

Maciej Bocheński

Publications and source records attributed to Maciej Bocheński.

2 recordsLinked to original sources

arXiv2022

On semisimple standard compact Clifford-Klein forms

In this paper 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.

math.DG↗

arXiv2018

Semisimple subalgebras in simple Lie algebras and a computational approach to the compact Clifford-Klein forms problem

In this paper we develop algorithms of finding homogeneous spaces of semisimple non-compact Lie groups which do not admit compact Clifford-Klein forms. We propose a computer program which checks if the given homogeneous space has a non-vanishing cohomological obstruction (found by Tholozan) to compact Clifford-Klein forms. By a numerical experiment we show that there is a large class of homogeneous spaces satisfying Tholozan's condition.

math.RT↗