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
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