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The rotation group SO(3) has as a universal cover the group SU(2), which is isomorphic to the group of versors in the quaternions. This is a double cover since the kernel has order 2. (cf the tangloids.) The unitary group U(n) is covered by the compact group T × SU(n) with the covering homomorphism given by p(z, A) = zA. The universal cover is ...
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