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 the constructed Lie algebras.
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