# Non-existence of standard compact Clifford-Klein forms of homogeneous spaces of exceptional Lie groups

## TL;DR

This paper employs computer-aided algorithms to prove the non-existence of standard compact Clifford-Klein forms for homogeneous spaces of exceptional Lie groups, supporting Kobayashi's conjecture.

## Contribution

It introduces a novel computational approach combining elimination algorithms and classification methods to establish non-existence results in this mathematical context.

## Key findings

- No standard compact Clifford-Klein forms exist for these spaces.
- The approach confirms Kobayashi's conjecture in this setting.
- Computational methods effectively eliminate possible forms.

## Abstract

We use a computer-aided approach to prove that there are no standard compact Clifford-Klein forms of homogeneous spaces of exceptional Lie groups. This yields further support for Kobayashi's conjecture about possible compact Clifford-Klein forms. On one hand, our approach is based on the algorithms developed in this work which eliminate the majority of possibilities. On the other hand, we complete the proof using the algorithmic methods of classifying semisimple subalgebras in simple real Lie algebras developed by Faccin and de Graaf, as well as by calculating invariants like a-hyperbolic rank.