The orientation-preserving diffeomorphism group
of the circle, Diff(S1
) admits a central extension
called the Virasoro group
. Its complexified Lie algebra
}i in Z
and c with Ln
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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