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:

    Let children know you are human. It’s important for children to see that parents are human and make mistakes. When you’re sorry about something you’ve said or done, apologize! But don’t sound guilt ridden. It is best when parents apologize in a manner that is straightforward and sincere.
    Saf Lerman (20th century)