Homogeneous Hypercomplex Structures I - the compact Lie groups

George Dimitrov; Vasil Tsanov

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arXiv · 1005.0172

Homogeneous Hypercomplex Structures I - the compact Lie groups

George Dimitrov·Vasil Tsanov

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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.

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George Dimitrov, Vasil Tsanov. 2012-04-24. Homogeneous Hypercomplex Structures I - the compact Lie groups. https://arxiv.org/abs/1005.0172

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