Spin(4) double cover
= Spin(4) double cover
{c}
{title2=$\operatorname{Spin}(4)\cong SU(2)\times SU(2)$}
Two <unit quaternions> act on Euclidean four-space by $q\mapsto aqb^{-1}$. This norm-preserving action maps onto the <SO(4) group>. Its kernel is precisely $(1,1)$ and $(-1,-1)$: a kernel pair must have equal entries commuting with every <quaternion>. The two simply connected <SU(2)> factors therefore form the universal spin cover.