Symplectic group
In
abstract algebra, the
symplectic group of degree
2n over a
field F (written as Sp(
n,
F)) is the
group of
2n by
2n symplectic matrices with entries from
F, with the group operation that of
matrix multiplication. This is a
subgroup of the
general linear group Gl(
n,
F).
If the field F is the field of real or complex numbers, then the symplectic group Sp(n,F) is a Lie group.
See also Symplectic space.