Abstract:
We define a new cohomology theory of associative algebras called semiinfinite cohomology in the derived categories' setting. We investigate the case of a small quantum group u, calculate semiinfinite cohomology spaces of the trivial u-module and express them in terms of local cohomology of the nilpotent cone for the corresponding semisimple Lie algebra. We discuss the connection between the semiinfinite homology of u and the conformal blocks' spaces.
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Received: 14 October 1996 / Accepted: 25 February 1997
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Arkhipov, S. Semiinfinite Cohomology of Quantum Groups . Comm Math Phys 188, 379–405 (1997). https://doi.org/10.1007/s002200050170
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DOI: https://doi.org/10.1007/s002200050170