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Virasoro algebra

The orientation-preserving diffeomorphism group of the circle, Diff(S1) admits a central extension called the Virasoro group. Its complexified Lie algebra is spanned by {Li}i in Z and c with Ln+L-n and c being real elements. c is called the central charge. The algebra satisfies
[Lm,Ln]=(n-m)Lm+n+c/12 (m3-m)δm,-n.

The factor of 1/12 is merely a matter of convention.

Note that the Virasoro algebra generates both a centrally extended orientation-preserving diffeomorphism group and a centrally extended orientation-preserving homeomorphism group of the circle. The difference lies in the topology chosen.

See also Kac-Moody algebra.

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