Abstract
We compute the homology of the Lie algebra W 1 of (polynomial) vector fields on the line with coefficients in symmetric powers of its adjoint representation. We also list the results obtained so far for the homology with coefficients in tensor powers and, in turn, use them for partially computing the homology of the Lie algebra of W 1-valued currents on the line.
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References
B. L. Feigin and B. L. Tsygan, “Riemann-Roch theorem and Lie algebra cohomology,” in: Proc. of the Winter School on Geometry and Physics (Srni, 9–16 January 1988), Rend. Circ. Mat. Palermo (2) Suppl., No. 21, 15–52 (1989).
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 40, No. 2, pp. 13–19, 2006
Original Russian Text Copyright © by V. V. Dotsenko
Supported in part by grant No. 2044.2003.2 of the President of the Russian Federation and by INTAS grant No. 03-3350.
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Dotsenko, V.V. Homology of the Lie algebra of vector fields on the line with coefficients in symmetric powers of its adjoint representation. Funct Anal Its Appl 40, 91–96 (2006). https://doi.org/10.1007/s10688-006-0015-2
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DOI: https://doi.org/10.1007/s10688-006-0015-2