Sur la cohomologie de l'algèbre de Lie des champs de vecteurs de contact formels

Claude Roger

Annales de l'institut Fourier (1980)

  • Volume: 30, Issue: 3, page 249-257
  • ISSN: 0373-0956

Abstract

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We prove the finiteness of the cohomology of the Lie algebra of formal vector fields in 2 n + 1 variables, respecting the universal contact form w = d x 0 + ∑ i = 1 n x i d x ‾ i .

How to cite

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Roger, Claude. "Sur la cohomologie de l'algèbre de Lie des champs de vecteurs de contact formels." Annales de l'institut Fourier 30.3 (1980): 249-257. <http://eudml.org/doc/74463>.

@article{Roger1980,
abstract = {Nous démontrons la finitude de la cohomologie de l’algèbre de Lie des champs de vecteurs formels à $2n+1$ variables, respectant la forme de contact universelle $w=dx_0+\sum ^n_\{i=1\}x_id\bar\{x\}_i$.},
author = {Roger, Claude},
journal = {Annales de l'institut Fourier},
keywords = {cohomology of vector fields; Gelfand-Fuks cohomology of formal contact- vectorfields},
language = {fre},
number = {3},
pages = {249-257},
publisher = {Association des Annales de l'Institut Fourier},
title = {Sur la cohomologie de l'algèbre de Lie des champs de vecteurs de contact formels},
url = {http://eudml.org/doc/74463},
volume = {30},
year = {1980},
}

TY - JOUR
AU - Roger, Claude
TI - Sur la cohomologie de l'algèbre de Lie des champs de vecteurs de contact formels
JO - Annales de l'institut Fourier
PY - 1980
PB - Association des Annales de l'Institut Fourier
VL - 30
IS - 3
SP - 249
EP - 257
AB - Nous démontrons la finitude de la cohomologie de l’algèbre de Lie des champs de vecteurs formels à $2n+1$ variables, respectant la forme de contact universelle $w=dx_0+\sum ^n_{i=1}x_id\bar{x}_i$.
LA - fre
KW - cohomology of vector fields; Gelfand-Fuks cohomology of formal contact- vectorfields
UR - http://eudml.org/doc/74463
ER -

References

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  1. [1] M. CHAPERON, Singularités en géométrie de contact, Astérisque, 59-60 (1978). Zbl0406.53034MR80k:58103
  2. [2] I.M. GELFAND, The Cohomology of infinite dimensional Lie algebras. Some questions of integral geometry, Actes du Congrès international des mathématiciens, Nice, 1970. 
  3. [3] I.M. GELFAND et B.A. FUKS, The Cohomology of the Lie algebra of formal vector fields, Izv. Akad. Nauk SSSR, 34 (1970), 322-337. Zbl0216.20302
  4. [4] I.M. GELFAND et B.A. FUKS, Upper bounds for cohomology of infinite dimensional Lie algebras, Functional analysis and its applications, vol. 4, n° 4, 1970. Zbl0224.18013MR44 #4792
  5. [5] C. GODBILLON, Cohomologies d'algèbres de Lie de champs de vecteurs, Séminaire Bourbaki 421, 1972. Zbl0296.17010
  6. [6] V. GUILLEMIN, D.G. QUILLEN, S. STERNBERG, The Classification of the irreducible complex algebras of infinite type, J. Analyse Math., t. 18 (1967), 107-112. Zbl0153.05903MR36 #221
  7. [7] S. KOBAYASHI, Transformation groups in differential geometry, Ergebnisse der Mathematik une ihrer Grenzgebiete, Band 70 (1972). Zbl0246.53031MR50 #8360
  8. [8] F. KAMBER et P. TONDEUR, Foliated bundles and characteristic classes, Lecture notes in math., 493 (1975). Zbl0308.57011MR53 #6587
  9. [9] A. LICHNEROWICZ, Cohomologie 1-différentiable des algèbres de Lie attachées à une variété symplectique ou de contact, J. Math. Pures et Appl., t. 53 (1974), 459-484. Zbl0317.53038MR51 #4315
  10. [10] M.V. LOZIK, On the Cohomologies of infinite dimensional Lie algebras of vector fields, Functional analysis and its applications, vol. 4, n° 2 (1970), 127. Zbl0212.28002
  11. [11] J. MORIMOTO et T. TANAKA, The Classification of real primitive infinite Lie algebras, Journal Math. Kyoto, (1970), 207-243. Zbl0211.05401MR42 #3133
  12. [12] J. PERCHIK, Cohomology of hamiltonian and related formal vector field Lie algebras, Topology. Zbl0343.58004
  13. [13] B.I. ROZENFELD, One dimensional cohomologies of a Lie algebra of contact vector fields, Functional analysis and its applications, vol. 4, n° 3 (1970), 171. Zbl0216.45601MR43 #4058
  14. [14] J. VEY, Rapport sur les champs symplectiques formels, Publ. Dépt. Math. Université de Lyon I, t. 13, fasc. 3 (1976). Zbl0373.57012MR57 #7619

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