2000/12/20 by Elena Poletaeva
Mathematics · #math.AG
published as Ann. Inst. Fourier (Grenoble) 51 (2001), no.3, 745-768. · 23 pages, TeX. To be published in Annales de l'Institut Fourier
arxiv created 2000/12/20 · arxiv updated 2009/11/30
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.