On semisimple standard compact Clifford-Klein forms

TL;DR

This paper classifies standard compact Clifford-Klein forms for certain semisimple Lie algebra triples, providing new examples of spaces with non-standard forms by leveraging Onishchik's decomposition results.

Contribution

It offers a complete classification of standard forms for triples where g = h + l and g is a sum of simple ideals, introducing new examples of non-standard forms.

Findings

Classification of standard compact Clifford-Klein forms for specified triples

New examples of reductive homogeneous spaces with non-standard forms

Application of Onishchik's decomposition results to classify forms

Abstract

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.