Giving the group $SO(3)$ to represent rotations in 3D space, what is exactly $SU(2)$ then? the formal relation between $SO(3)$ and $SU(2)$ was given by: $SO(3)\cong SU(2)/\Bbb{Z}_2$ and informally it was mentioned that $SU(2)$ is a 'double cover' of $SO(3)$, I didn't understand both since I don't understand what $\cong$ in group theory means and what $SU(2)$ actually represents, I know it is a silly question I tried the web and couldn't fully understand, any help would be much appreciated.
2026-03-25 16:06:51.1774454811
On the relation between SO(3) and SU(2) groups
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