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

2019/01/14 by Bochenski, Maciej, Jastrzebski, Piotr, Tralle, Aleksy
#17B20 #22E40 #22F30 #57S30 #65-05 #65F #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.04341

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.

Related

• A solution of the problem of standard compact Clifford-Klein forms
• Obstructions to the existence of compact Clifford-Klein forms for\n tangential symmetric spaces
• Compactification of certain Clifford-Klein forms of reductive homogeneous spaces
• Compact Clifford-Klein forms of homogeneous spaces of SO(2,n)
• Volume and non-existence of compact Clifford-Klein forms