Special unitary group

In abstract algebra, the special unitary group of degree n over a field F (written as SU(n,F)) is the group of n by n unitary matrices with determinant 1 and entries from F, with the group operation that of matrix multiplication. This is a subgroup of the unitary group U(n,F), itself a subgroup of the general linear group Gl(n,F).

If the field F is the field of real or complex numbers, then the special unitary group SU(n,F) is a Lie group.