The Virasoro algebra is defined as where the [.,.] are Poisson brackets. My text claims that using we can generate , which is a subalgebra of the Virasoro algebra. I don't see how this is a subalgebra is isomorphic (is that the right word?) with .

Any takers?

-Dan

Edit: Oh! As usual I saw the answer after I posted. has three degrees of freedom as does . I get it now.