no. 3
Semi-infinite cohomology and superconformal algebras
[Cohomologie semi-infinie et algèbres superconformes]
Poletaeva, Elena1
1 Lund University, Centre for Mathematical Sciences, Box 118, 221 00 Lund (Suède)
Annales de l'Institut Fourier, Tome 51 (2001) no. 3, pp. 745-768.

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.

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.

DOI : 10.5802/aif.1835
Classification : 17B55, 17B70, 81R10, 14F40
Keywords: Weil complex, semi-infinite cohomology, superconformal algebra, Kähler geometry
Mot clés : complexe de Weil, cohomologie semi-infinie, algèbre superconforme, géométrie kählérienne

Poletaeva, Elena 1

1 Lund University, Centre for Mathematical Sciences, Box 118, 221 00 Lund (Suède) 
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Poletaeva, Elena. Semi-infinite cohomology and superconformal algebras. Annales de l'Institut Fourier, Tome 51 (2001) no. 3, pp. 745-768. doi : 10.5802/aif.1835. https://aif.centre-mersenne.org/articles/10.5802/aif.1835/

[Ad] M. Ademollo; L. Brink; A. D' Adda; R. D' Auria; E. Napolitano; S. Sciuto; E. Del; Giudice; P. Di; Vecchia; S. Ferrara; F. Gliozzi; R. Musto; R. Rettorino Dual strings with U(1) colour symmetry, Nucl. Phys., Volume B111 (1976), pp. 77-110 | DOI

[Ak] F. Akman Some cohomology operators in 2-D field theory, Proceedings of the conference on Quantum topology (Manhattan, KS, 1993) (1994), pp. 1-19 | Zbl

[Fe] B. L. Feigin Private communication

[FF] B. Feigin; E. Frenkel Semi-infinite Weil Complex and the Virasoro Algebra, Commun. Math. Phys., Volume 137 (1991), pp. 617-639 | DOI | MR | Zbl

[FF] B. Feigin; E. Frenkel Erratum "Semi-infinite Weil Complex and the Virasoro Algebra", Commun. Math. Phys., Volume 147 (1992), pp. 647-648 | DOI | MR | Zbl

[FGZ] I. Frenkel; H. Garland; G. Zuckerman Semi-infinite cohomology and string theory, Proc. Natl. Acad. Sci. U.S.A., Volume 83 (1986), pp. 8442-8446 | DOI | MR | Zbl

[FST] B. L. Feigin; A. M. Semikhatov; I. Yu. Tipunin Equivalence between chain categories of representations of affine sl (2) and N=2 superconformal algebras, J. Math. Phys., Volume 39 (1998) no. 7, pp. 3865-3905 | DOI | MR | Zbl

[Fu] D. B. Fuks Cohomology of infinite-dimensional Lie algebras, Consultants Bureau, New York and London, 1986 | MR | Zbl

[G] E. Getzler Two-dimensional topological gravity and equivariant cohomology, Commun. Math. Phys., Volume 163 (1994) no. 3, pp. 473-489 | DOI | MR | Zbl

[GH] P. Griffiths; J. Harris Principles of algebraic geometry, Wiley-Interscience Publ., New York, 1978 | MR | Zbl

[KL] V. G. Kac; J. W. van de Leur; S. J. Gates et al., editors On Classification of Superconformal Algebras, Strings-88 (1989), pp. 77-106 | Zbl

[P1] E. Poletaeva Semi-infinite Weil complex and N = 2 superconformal algebra I (Preprint MPI 97-78)

[P1] E. Poletaeva Semi-infinite Weil complex and superconformal algebras II (Preprint MPI 97-79)

[P2] E. Poletaeva Superconformal algebras and Lie superalgebras of the Hodge theory (Preprint MPI, p. 99-136) | MR | Zbl

[P3] E. Poletaeva Semi-infinite cohomology and superconformal algebras, Comptes Rendus de l'Académie des Sciences, Série I, Volume t. 326 (1998), pp. 533-538 | MR | Zbl

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