What's the correct way to state the relationship between these two Lie groups? One is the "covering group" of the other, right? Okay, then - what's that mean, to a non-expert?(adsbygoogle = window.adsbygoogle || []).push({});

I know the basics, i.e. SO(3) can be represented by rotation matrices in 3-space, and U(2) does the same in a complex 2-space, but how are the two connected?

What I'd really like to know is how to explain to non-physicists (like the engineers I work with) how it is that quaternions are used to represent body orientations in 3-space and why the angles pick up a factor of 1/2. I know it's connected to the business of a 2-pi rotation in complex 2-space picking up a factor of -1 so that you have to do a rotation by 4-pi to get back to your initial orientation ... but I don't really know what that means.

Any helpful pictures or explanations?

Thanks,

Bruce

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# U(2) and SO(3)

**Physics Forums | Science Articles, Homework Help, Discussion**