Symplectic Group - Important Subgroups

Important Subgroups

The symplectic group Sp(n) is sometimes written as USp(2n) which is convenient for the following equations. The symplectic group comes up in quantum physics as a symmetry on poisson brackets so it is important to understand its subgroups. Some main subgroups are:

The symplectic groups are also subgroups of various Lie groups:

There are also the isomorphisms of the Lie algebras usp(4) = o(5) and usp(2) = o(3) = su(2).

Read more about this topic:  Symplectic Group

Famous quotes containing the word important:

    Ecouraging a child means that one or more of the following critical life messages are coming through, either by word or by action: I believe in you, I trust you, I know you can handle this, You are listened to, You are cared for, You are very important to me.
    Barbara Coloroso (20th century)