Extensions of Virasoro group and Virasoro algebra by modules of tensor-densities on $S^1$

V. Ovsienko; C. Roger

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arXiv · hep-th/9409067

Extensions of Virasoro group and Virasoro algebra by modules of tensor-densities on $S^1$

V. Ovsienko·C. Roger

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Abstract

We classify non-trivial (non-central) extensions of the group $Diff^+(S^1)$ of all diffeomorphisms of the circle preserving its orientation and of the Lie algebra $Vect (S^1)$ of vector fields on $S^1$, by the modules of tensor-densities on $S^1$. The result is: 4 non-trivial extensions of $Diff^+(S^1)$ and 7 non-trivial extensions of $Vect (S^1)$. Analogous results hold for the Virasoro group and the Virasoro algebra. We also classify central extensions of constructed Lie algebras. CPT-94/P.3024

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V. Ovsienko, C. Roger. 1994-09-12. Extensions of Virasoro group and Virasoro algebra by modules of tensor-densities on $S^1$. https://arxiv.org/abs/hep-th/9409067

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