 Adjoint double cover from SU(2) to SO(3)

ID: adjoint-double-cover-from-su-2-to-so-3

S U (2)

on its three-dimensional real Lie algebra of traceless skew-Hermitian matrices preserves

- tr (A B)

and defines a surjection

S U (2) ⟶ SO (3)

with kernel

{\pm I_{2}}

. It is the universal double covering of

SO (3)

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