The Virasoro algebra is defined as $\displaystyle \left [ L_m, L_n \right ] = i (m - n) L_{m + n}$ where the [.,.] are Poisson brackets. My text claims that using we can generate $\displaystyle SL(2, \mathbb{R} )$, 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 $\displaystyle SL(2, \mathbb{R} )$.

Any takers?

-Dan

Edit: Oh! As usual I saw the answer after I posted. $\displaystyle SL(2, \mathbb{R} )$ has three degrees of freedom as does $\displaystyle \{ L_{-1}, L_0, L_1 \}$. I get it now.