Special unitary Lie algebra
= Special unitary Lie algebra
{title2=$\mathfrak{su}(n)$}
The real <Lie algebra> of the <special unitary group> consists of traceless <skew-Hermitian matrices>. Differentiating unitarity and determinant one gives the two constraints; exponentiating any such matrix proves their sufficiency. The <commutator> is again skew-Hermitian and traceless. Its real dimension is $n^2-1$, and its complexification is $\mathfrak{sl}_n(\mathbb C)$.