Semi-infinite homological algebra

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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.

Original languageEnglish (US)
Pages (from-to)103-146
Number of pages44
JournalInventiones Mathematicae
Issue number1
StatePublished - Dec 1 1993


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