Homogeneous Hypercomplex Structures I - the compact Lie groups
Differential Geometry
2015-03-17 v2 Group Theory
Abstract
We introduce a remarkable subset "the stem" of the set of positive roots of a reduced root system. The stem determines several interesting decompositions of the corresponding reductive Lie algebra. It gives also a nice simple three dimensional subalgebra and a "Cayley transform". In the present paper we apply the above devices to give a complete classification of invariant hypercomplex structures on compact Lie groups.
Cite
@article{arxiv.1005.0172,
title = {Homogeneous Hypercomplex Structures I - the compact Lie groups},
author = {George Dimitrov and Vasil Tsanov},
journal= {arXiv preprint arXiv:1005.0172},
year = {2015}
}
Comments
In the second version we have made several proofs more transparent. We have removed from the introduction some things, which are presented in a better way in the introduction of part II