Homogeneous Hypercomplex Structures I - the compact Lie groups
arXiv:1005.0172
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.
arXiv commentIn 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