Semiinfinite Cohomology of Quantum Groups
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 umodule 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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 1997
 DOI:
 10.1007/s002200050170
 arXiv:
 arXiv:qalg/9601026
 Bibcode:
 1997CMaPh.188..379A
 Keywords:

 Mathematics  Quantum Algebra
 EPrint:
 24 pages