Poletaeva, Elena Semi-infinite cohomology and superconformal algebras. (English. Abridged French version) Zbl 0923.17022 C. R. Acad. Sci., Paris, Sér. I, Math. 326, No. 5, 533-538 (1998). Let \(\widetilde {\mathfrak g}={\mathfrak g}\otimes\mathbb{C}[t,t^{-1}]\) be a loop algebra and \[ W^{{\infty\over 2}+*}=S^{{\infty\over 2}+*}(\widetilde g)\otimes \wedge^{ {\omega\over 2}+*} (\widetilde{\mathfrak g}) \] the semi-infinite Weil complex of \(\widetilde{\mathfrak g}\). The Lie algebra \(\widetilde {\mathfrak g}\) acts on \(W^{{\infty\over 2}+*}\), projective actions defined on each multiple via normal ordering produce an ordinary action on the product. The author shows that the \(N=2\) superconformal algebra also acts on \(W^{{\infty\over 2}+*}\), generators of the action are constructed as series of normally ordered monomials of second degree in elements of \(\widetilde {\mathfrak g}\).Similarly defined actions are constructed also for the relative semi-infinite Weil complex. The detailed exposition of the results is available in MPI-Bonn preprints. Reviewer: A.Rudakov (Trondheim) Cited in 2 Documents MSC: 17B56 Cohomology of Lie (super)algebras 17B68 Virasoro and related algebras 17B65 Infinite-dimensional Lie (super)algebras Keywords:Kac-Moody Lie algebra; loop algebra; superconformal algebra; semi-infinite Weil complex PDFBibTeX XMLCite \textit{E. Poletaeva}, C. R. Acad. Sci., Paris, Sér. I, Math. 326, No. 5, 533--538 (1998; Zbl 0923.17022) Full Text: DOI