Semi-infinite homological algebra

• DOI: 10.1007/bf01244304
• Publication Date: 2005-02-26T09:24:09Z
• Authors: Alexander A. Voronov
• Keywords: 510.mathematics; 0103 physical sciences; 0101 mathematics; 01 natural sciences; Article

The paper provides a homological algebraic foundation for semi-infinite cohomology. It is proved that semi-infinite cohomology of infinite dimensional Lie algebras is a two-sided derived functor of a functor that is intermediate between the functors of invariants and coinvariants. The theory of two-sided derived functors is developed. A family of modules including a module generalizing the universal enveloping algebra appropriate to the setting of two sided derived functors is introduced. A vanishing theorem for such modules is proved.