Semiinfinite cohomology of quantum groups

Details Semiinfinite cohomology of quantum groups Semiinfinite cohomology of quantum groups

1996-01-24

arxiv.org/abs/q-alg/9601026v1

Mathematics

Quantum Algebra

24 pages

Scientific paper

10.1007/s002200050170

In this paper we develop a new homology theory of associative algebras called semiinfinite cohomology in a derived category setting. We show that in the case of small quantum groups the zeroth semiinfinite cohomology of the trivial module is closely related to the conformal blocks' spaces. We provide a description of the semiinfinite cohomology spaces of the trivial module over a small quantum group in terms of distributions on the nilpotent cone of the corresponding semisimple Lie algebra.

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