On the non-existence of left-invariant hypercomplex structures on SU(2)⁴ⁿ

2025/05/27 by Pham, David N.
#32Q60 #53C15 #53C26 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.21766

Abstract

Using elementary algebraic arguments, it is shown that SU(2)^m:=SU(2)× ⋯ × SU(2) (m times) admits no left-invariant hypercomplex structures for all m≥ 1. This result answers (in a clear and easily accessible way) the question of whether every compact Lie group of dimension 4n admits a left-invariant hypercomplex structure. The aforementioned question has apparently been the source of some confusion in the recent literature.

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