A characterization of the differential in semi-infinite cohomology

Details A characterization of the differential in semi-infinite cohomology A characterization of the differential in semi-infinite cohomology

1993-02-27

arxiv.org/abs/hep-th/9302141v1

Physics

High Energy Physics

High Energy Physics - Theory

19 pages (to appear in Journal of Algebra)

Scientific paper

Semi-infinite cohomology is constructed from scratch as the proper generalization of finite dimensional Lie algebra cohomology. The differential d and other operators are realized as universal inner deri- vations of a completed algebra, which acts on any appropriate semi-infinite complex. In particular, d is shown to be the unique derivation satisfying the "Cartan identity" and certain natural degree conditions. The proof that d is square-zero may well be the shortest (arguably, the only) one in print.

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