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

David N. Pham

Using elementary algebraic arguments, it is shown that $SU(2{)}^m:=SU(2)\times \cdots \times SU(2)$ ($m$ times) admits no left-invariant hypercomplex structures for all $m\ge 1$. T…