2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60618We 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.23 pages, TeX. To be published in Annales de l'Institut FourierAlgebraic Geometrytext