Journal of Lie Theory

no. 1
Explicit Formulae for Cocycles of Holomorphic Vector Fields with Values in λ Densities
Journal of Lie Theory, Volume 11 (2001) no. 1, pp. 173-184
We give explicit formulae for the generators of H2( Hol (Σr),  Fλ (Σr)) in terms of affine and projective connections, Σr 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 ["Generalizations of Virasoro group and Virasoro algebra through extensions by modules of tensor-densities on S1, Indag. Math., N.S. 9 (1998) 277--288] and globalizing them by their transformation property.
DOI: 10.5802/jolt.228
Classification: 17B56, 17B66, 30F30
Keywords: Lie algebra of vector fields, densities, 2-cocycles, punctured Riemann surface, Krichever-Novikov algebras 
@article{JOLT_2001_11_1_a9,
     author = {F. Wagemann},
     title = {Explicit {Formulae} for {Cocycles} of {Holomorphic} {Vector} {Fields} with {Values} in \ensuremath{\lambda} {Densities}},
     journal = {Journal of Lie Theory},
     pages = {173--184},
     year = {2001},
     volume = {11},
     number = {1},
     doi = {10.5802/jolt.228},
     zbl = {1055.17010},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.228/}
}
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F. Wagemann. Explicit Formulae for Cocycles of Holomorphic Vector Fields with Values in λ Densities. Journal of Lie Theory, Volume 11 (2001) no. 1, pp. 173-184. doi: 10.5802/jolt.228

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