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Thread: Virasoro Algebra

  1. #1
    Forum Admin topsquark's Avatar
    Jan 2006
    Wellsville, NY

    Virasoro Algebra

    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?


    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.
    Last edited by topsquark; Jul 30th 2013 at 11:57 AM.
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