Semi-infinite cohomology and superconformal algebras

Details Semi-infinite cohomology and superconformal algebras Semi-infinite cohomology and superconformal algebras

2000-12-20

arxiv.org/abs/math/0012195v1

Ann. Inst. Fourier (Grenoble) 51 (2001), no.3, 745-768.

Mathematics

Algebraic Geometry

23 pages, TeX. To be published in Annales de l'Institut Fourier

Scientific paper

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 K\"ahler geometry.

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