Symplectic group

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(2n,F).

If the field F is the field of real or complex numbers, then the symplectic group Sp(n,F) is a Lie group.