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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.

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, 08544-1000, Princeton, NJ, USA

    Alexander A. Voronov

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  1. Alexander A. Voronov
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Oblatum 28-IX-1992 & 11-I-1993

Research supported in part by NSF grant DMS-8505550

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Voronov, A.A. Semi-infinite homological algebra. Invent Math 113, 103–146 (1993). https://doi.org/10.1007/BF01244304

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