2
$\begingroup$

I know there is a double covering map between SU(2) and SO(3) but I have no idea how I would go about proving this or showing this.

can someone point me in the right direction please?

  • 1
    The [projective special unitary group](http://en.wikipedia.org/wiki/Projective_unitary_group#Examples) $PSU(2)=SU(2)/\{-1,1\}$ is isomorphic to $SO(3)$. $SU(2)$ is the [double cover](http://en.wikipedia.org/wiki/Covering_group#Examples) of $SO(3)$.2012-05-04
  • 0
    Sorry, I'm might have introduced something wrong in your question by replacing *double map* by *isomorphism*. What do you mean by *double map* ?2012-05-04
  • 0
    @Lierre: Even if in some other cases it might conceivably be warranted to replace "double map" by "isomorphism" without knowing the intended meaning (which seems unlikely), it's certainly a bad idea to then summarize your edit with "spelling".2012-05-04
  • 0
    @joriki — I agree2012-05-04
  • 2
    @steven: Take a look at [quaternions](http://en.wikipedia.org/wiki/Quaternion) and [their relationship with rotations](http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation); that's a useful way to understand the connection between $SU(2)$ and $SO(3)$.2012-05-04

0 Answers 0