Cross-product Lie algebra
= Cross-product Lie algebra
{title2=$(\mathbb R^3,\times)$}
The <vector space> $\mathbb R^3$ with the <cross product> as <Lie bracket>. The vector triple-product identity proves the <Jacobi identity>. The map $x\mapsto-(i/2)x\cdot\sigma$ is a <Lie algebra isomorphism> to the compact real <SU(2) Lie algebra>, using the <Pauli matrix commutator identity>.