Explicit formulae for cocycles of holomorphic vector fields with values in \(\lambda\) densities (Q2718665)
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scientific article; zbMATH DE number 1596873
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Explicit formulae for cocycles of holomorphic vector fields with values in \(\lambda\) densities |
scientific article; zbMATH DE number 1596873 |
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4 June 2001
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Lie algebra of vector fields
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densities
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2-cocycles
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punctured Riemann surface
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Krichever-Novikov algebras
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Explicit formulae for cocycles of holomorphic vector fields with values in \(\lambda\) densities (English)
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The subject of this paper is cohomology of a Lie algebra of holomorphic vector fields on a punctured Riemann surface \(\Sigma_r\), with coefficients in a module of holomorphic \(\lambda\)-densities on \(\Sigma_r\).NEWLINENEWLINEResults about this cohomology were obtained by \textit{N.~Kawazumi} [Ann. Inst. Fourier 43, 655--712 (1993; Zbl 0782.57019)], but explicit cocycles were not known. Here they are provided for the second cohomology. NEWLINENEWLINEThis is motivated by a search for generalizations of Krichever-Novikov algebras as corresponding abelian extensions, analogous to the generalization of Virasoro algebras by \textit{V.~Ovsienko} and \textit{C.~Roger} [Indag.~Math. 9, 277--288 (1998; Zbl 0932.17029)].
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