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Semi-infinite cohomology and superconformal algebras. (English) Zbl 1067.17012

Summary: We describe representations of certain superconformal algebras in the semi-infinite Weil complex related to the loop algebra of a complex finite-dimensional Lie algebra and in the semi-infinite cohomology. We show that in the case where the Lie algebra is endowed with a non-degenerate invariant symmetric bilinear form, the relative semi-infinite cohomology of the loop algebra has a structure, which is analogous to the classical structure of the de Rham cohomology in Kähler geometry.

MSC:

17B68 Virasoro and related algebras
17B56 Cohomology of Lie (super)algebras
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