Homogeneous Hypercomplex Structures I - the compact Lie groups

2010/05/02 by George Dimitrov, Dimitrov, George, Vasil Tsanov +1
Chemistry · Mathematics · Physics and Astronomy · #17B22 #22E46 #53Cxx #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR) #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1005.0172

openalex publication_date 2010/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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