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.