The double covering of compact quantum group $S{O}_q(4)$

Abstract

We show that ${\mathbb{Z}}_2$ is a quantum normal subgroup of $S{U}_q(2)\times S{U}_q(2)$ and that the quotient group is isomorphic to $S{O}_q(4)$, thereby establishing that $S{U}_q(2)\times S{U}_q(2)$ is a double cover of $S{O}_q(4)$.

14 pages