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

Friedrich Wagemann (1)

1 IGD - Institut Girard Desargues

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.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Variables complexes [math.CV]

Friedrich Wagemann. Explicit Formulae for Cocycles of Holomorphic Vector Fields with values in lambda-Densities. Journal of Lie Theory, 2001, 114, pp.173-184. ⟨hal-00008866⟩