SU(2)^m carries no left-invariant hypercomplex structure for any m≥1, proved by direct Nijenhuis-tensor computations.
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On the non-existence of left-invariant hypercomplex structures on $SU(2)^{4n}$
SU(2)^m carries no left-invariant hypercomplex structure for any m≥1, proved by direct Nijenhuis-tensor computations.