Indefinite special unitary group
= Indefinite special unitary group
{title2=$SU(p,q)$}
The <indefinite special unitary group> preserves a <Hermitian> form of signature $(p,q)$ and has <determinant> one: $M^\dagger J M=J$, where $J=\operatorname{diag}(I_p,-I_q)$. With both $p,q$ positive it is noncompact, unlike the group preserving a positive-definite form. Its <Lie algebra> satisfies $X^\dagger J+JX=0$ and $\operatorname{Tr}X=0$.