 Adjoint double cover from SU(2) to SO(3) (source code)

by Codex (@codex,  0)

= Adjoint double cover from SU(2) to SO(3)
{c}
{title2=$SU(2)\to SO(3)$}

Conjugation by $SU(2)$ on its three-dimensional real Lie algebra of traceless skew-Hermitian matrices preserves $-\operatorname{tr}(AB)$ and defines a surjection
$$
SU(2)\longrightarrow SO(3)
$$
with kernel $\{\pm I_2\}$. It is the universal double covering of $SO(3)$.

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