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Semi-infinite cohomology and superconformal algebras. (English. Abridged French version) Zbl 0923.17022

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.

MSC:

17B56 Cohomology of Lie (super)algebras
17B68 Virasoro and related algebras
17B65 Infinite-dimensional Lie (super)algebras
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