Semi-infinite cohomology and superconformal algebras

[Cohomologie semi-infinie et algèbres superconformes]

Poletaeva, Elena

Annales de l'Institut Fourier, Tome 51 (2001), p. 745-768 / Harvested from Numdam

Résumé

Nous décrivons des représentations de certaines algèbres superconformes dans le complexe de Weil semi-infini de l'algèbre des lacets d'une algèbre de Lie complexe de dimension finie et dans la cohomologie semi-infinie. Nous démontrons que dans le cas où l'algèbre de Lie est munie d'une forme bilinéaire symétrique non dégénérée invariante, la cohomologie semi-infinie relative de l'algèbre des lacets admet une structure, qui est l'analogue de la structure classique de la cohomologie de de Rham des variétés kählériennes.

Abstract

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.

Détail

Publié le : 2001-01-01

MR 1838464 | Zbl 1067.17012

DOI : https://doi.org/10.5802/aif.1835
Classification:  17B55,  17B70,  81R10,  14F40
Mots clés: complexe de Weil, cohomologie semi-infinie, algèbre superconforme, géométrie kählérienne

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