Semi-infinite cohomology and superconformal algebras
Annales de l'Institut Fourier, Volume 51 (2001) no. 3, p. 745-768

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.

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.

DOI : https://doi.org/10.5802/aif.1835
Classification:  17B55,  17B70,  81R10,  14F40
Keywords: Weil complex, semi-infinite cohomology, superconformal algebra, Kähler geometry
@article{AIF_2001__51_3_745_0,
     author = {Poletaeva, Elena},
     title = {Semi-infinite cohomology and superconformal algebras},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {51},
     number = {3},
     year = {2001},
     pages = {745-768},
     doi = {10.5802/aif.1835},
     zbl = {1067.17012},
     mrnumber = {1838464},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2001__51_3_745_0}
}
Poletaeva, Elena. Semi-infinite cohomology and superconformal algebras. Annales de l'Institut Fourier, Volume 51 (2001) no. 3, pp. 745-768. doi : 10.5802/aif.1835. http://www.numdam.org/item/AIF_2001__51_3_745_0/

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