Semi-infinite cohomology and superconformal algebras

Elena Poletaeva[1]

  • [1] Lund University, Centre for Mathematical Sciences, Box 118, 221 00 Lund (Suède)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 3, page 745-768
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Poletaeva, Elena. "Semi-infinite cohomology and superconformal algebras." Annales de l’institut Fourier 51.3 (2001): 745-768. <http://eudml.org/doc/115928>.

@article{Poletaeva2001,
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.},
affiliation = {Lund University, Centre for Mathematical Sciences, Box 118, 221 00 Lund (Suède)},
author = {Poletaeva, Elena},
journal = {Annales de l’institut Fourier},
keywords = {Weil complex; semi-infinite cohomology; superconformal algebra; Kähler geometry},
language = {eng},
number = {3},
pages = {745-768},
publisher = {Association des Annales de l'Institut Fourier},
title = {Semi-infinite cohomology and superconformal algebras},
url = {http://eudml.org/doc/115928},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Poletaeva, Elena
TI - Semi-infinite cohomology and superconformal algebras
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 3
SP - 745
EP - 768
AB - 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.
LA - eng
KW - Weil complex; semi-infinite cohomology; superconformal algebra; Kähler geometry
UR - http://eudml.org/doc/115928
ER -

References

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  9. V. G. Kac, J. W. van de Leur, On Classification of Superconformal Algebras, Strings-88 (1989), 77-106, World Scientific Zbl0938.17500
  10. E. Poletaeva, Semi-infinite Weil complex and N = 2 superconformal algebra I Zbl1067.17012
  11. E. Poletaeva, Superconformal algebras and Lie superalgebras of the Hodge theory Zbl1044.17017MR1976379
  12. E. Poletaeva, Semi-infinite cohomology and superconformal algebras, Comptes Rendus de l'Académie des Sciences, Série I t. 326 (1998), 533-538 Zbl0923.17022MR1649528
  13. I. Frenkel, H. Garland, G. Zuckerman, Semi-infinite cohomology and string theory, Proc. Natl. Acad. Sci. U.S.A. 83 (1986), 8442-8446 Zbl0607.17007MR865483
  14. B. Feigin, E. Frenkel, Erratum "Semi-infinite Weil Complex and the Virasoro Algebra", Commun. Math. Phys. 147 (1992), 647-648 Zbl0753.17033MR1175498
  15. E. Poletaeva, Semi-infinite Weil complex and superconformal algebras II Zbl1067.17012

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