Explicit Formulae for Cocycles of Holomorphic Vector Fields with values in lambda-Densities

Physics – Mathematical Physics

Scientific paper

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10 pages, submitted in J. Lie Theory, replaced version contains minor changes

Scientific paper

We give explicit formulae for the generators of H^2(Hol(\Sigma_r,{\cal
F}_{\lambda}(\Sigma_r)) in terms of affine and projective connections. This is
done using the cocycles of V. Ovsienko and C. Roger for the case of the circle
and globalizing them to an open Riemann surface \Sigma_r.

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