Whoops, fixed, thanks. It’s this question.

]]>I didn’t draw it! I stole it from Wikipedia.

]]>At some point I will try to talk about spin and angular momentum, although I still have to digest it a little. For the special case of SO(3) the Clifford algebra is just the quaternions anyway, which is the next post. But I have to admit I have no intuition for what the meaning of the Clifford algebra is in general. It seems to be geometric and physical in nature.

]]>I would like to remark that to find the fundamental group of SO(3) one might also take the approach of studying the Spin(3) directly, i.e. as a group sitting inside a Clifford Algebra (this is also very useful from representation-theoretic point of view). Or if one wants to omit the CA stuff, one can just note that Spin(3) is isomorphic to unit quaternions and start from there. Ultimately all of these approaches are of course connected but I suppose some of the proofs can be shorter and/or cleaner.

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