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Journal of Lie Theory, Vol. 11, No. 1, pp. 173-184 (2001)
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Explicit formulae for cocycles of holomorphic vector fields with values in $\lambda$ densities

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Friedrich Wagemann

Institut G. Desargues

Université C. Bernard Lyon 1

43, bd du 11 novembre 1918

F-69622 Villeurbanne Cedex

France

wagemann@desargues.univ-lyon1.fr

**Abstract:** In this article, 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, $\Sigma_r$ being a compact Riemann surface punctured in $r$ points This is done using the cocycles which have been evidenced by V. Ovsienko and C. Roger in [13] and globalizing them by their transformation property.

**Classification (MSC2000):** 17B56, 17B65, 17B66, 17B68

**Full text of the article:**

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