Homogeneous Hypercomplex Structures II - Coset Spaces of compact Lie Groups

TL;DR

This paper classifies hypercomplex manifolds with transitive compact automorphism groups using reductive group theory, extending previous work with a focus on coset spaces of compact Lie groups.

Contribution

It provides a complete classification of such hypercomplex manifolds, utilizing the concept of 'stem' in root systems, advancing the understanding of their geometric structure.

Findings

Complete classification of hypercomplex manifolds with transitive compact automorphism groups

Use of reductive group structure theory and 'stem' of root systems in proofs

Description of spaces as coset spaces of compact Lie groups

Abstract

We obtain a complete classification of hypercomplex manifolds, on which a compact group of automorphisms acts transitively. The description of the spaces as well as the proofs of our results use only the structure theory of reductive groups, in particular the notion of "stem" of a reduced root system, introduced in the first paper of this series.