Semisimple subalgebras in simple Lie algebras and a computational approach to the compact Clifford-Klein forms problem
Representation Theory
2019-09-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1804.03484,
title = {Semisimple subalgebras in simple Lie algebras and a computational approach to the compact Clifford-Klein forms problem},
author = {Maciej Bocheński and Piotr Jastrzębski and Anna Szczepkowska and Aleksy Tralle and Artur Woike},
journal= {arXiv preprint arXiv:1804.03484},
year = {2019}
}