English

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}
}