Essential extensions of some infinite dimensional lie algebras

  • J. A. Pereira da Silva
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1251)


Vector Field Poisson Structure Linear Connection Poisson Manifold Essential Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, D. Sternheimer, Deformation Theory and Quantization I, Ann. of Physics 111, p. 61–110 (1978).MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    M. Cahen, M. de Wilde, S. Gutt, Local cohomology of the algebra of C -functions on a symplectic manifold, Lett. in Math. Phys. 4, p. 157–167 (1980).CrossRefzbMATHGoogle Scholar
  3. [3]
    M. Flato, A. Lichnerowicz, D. Sternheimer, Deformations of Poisson Brackets, Dirac Brackets and Applications, J. Math. Phys. 17, p. 1754–1762 (1976).MathSciNetCrossRefGoogle Scholar
  4. [4]
    M. Flato et A. Lichnerowicz, Cohomologie des représentations définies par la dérivation de Lie et à valeurs dans les formes de l'algèbre de Lie des champs de vecteurs d'une variété différentiable. Premiers espaces de cohomologie. Applications. C.R. Acad. Sc. Paris, t. 291, p. 331–335 (1980).MathSciNetzbMATHGoogle Scholar
  5. [5]
    S. Gutt, Second and troisième espaces de cohomologie différentiable de l'algèbre de Lie de Poisson d'une variété symplectique, Ann. Inst. A. Poincaré 33, p. 1–31 (1980).MathSciNetzbMATHGoogle Scholar
  6. [6]
    F. Guedira et A. Lichnerowicz, Géométrie des algèbres de Lie localles de Kirillov, J. Math. pures et appl., 63, p. 407–484 (1984).MathSciNetzbMATHGoogle Scholar
  7. [7]
    A.A. Kirillov Local Lie algebras, Russ. Math. Surveys, 31, p. 55–57 (1976).MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    A. Lichnerowicz, Algèbre de Lie des automorphismes infinitésimaux d'une structure unimodulaire, Ann. Inst. Fourier, 24, p. 219–266 (1974).MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    A. Lichnerowicz, Les variétés de Poisson et leurs algèbres de Lie associées, J. Diff. Geom. 12, p. 253–300 (1977).MathSciNetzbMATHGoogle Scholar
  10. [10]
    A. Lichnerowicz, Les variétés de Jacobi et leurs algèbres de Lie associées, J. Math. pures et appl., 51, p. 453–488 (1978).MathSciNetzbMATHGoogle Scholar
  11. [11]
    A. Lichnerowicz, Existence et equivalence de deformations associatives associées à une variété symplectique, Lecture Notes in Mathe matics no 836, Springer, p. 177–185 (1979).Google Scholar
  12. [12]
    A. Lichnerowicz, Deformations and Quantization, Lectures Notes in Mathematics no 836, Springer, p. 366–374 (1979).Google Scholar
  13. [13]
    A. Lichnerowicz, Variétés de Poisson et feuilletages, Ann. Fac. Sc. Toulouse, 4, p. 195–262 (1982).MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    A. Lichnerowicz, Cohomologies attachées à une variété de contact et applications, J. Math. pures et appl. 62, p. 269–304 (1983).MathSciNetzbMATHGoogle Scholar
  15. [15]
    C.-M. Marle, Poisson Manifolds in Mechanics, in "Biffurcation theory, mechanics and physics", C.P. Bruter, A. Aragnol and A. Lichnerowicz, eds., Reidel (Dordrecht, 1983).Google Scholar
  16. [16]
    C.-M. Marle, Contact Manifolds, Canonical Manifolds and the Hamilton-Jacobi Method in Analytical Mechanics, Proc. of the IUTAM-ISIMM Symposium on Modern Developments in Analytical Mechanics, S. Benenti, M. Francaviglia and A. Lichnerowicz, eds., (Torino, 1983).Google Scholar
  17. [17]
    C.-M. Marle, Quelques propriétés des variétés de Jacobi (preprint).Google Scholar
  18. [18]
    H.J. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. Am. Math. Soc., 180, p. 171–188 (1973).MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    M. de Wilde et P. Lecomte, Cohomology of the Lie algebra of smooth vector fields of a manifold, associated to the Lie derivative of smooth forms, J. Math. pures et appl. 62, p. 197–214 (1983).MathSciNetzbMATHGoogle Scholar
  20. [20]
    A. Weinstein, The local structure of Poisson manifolds, J. Diff. Geom., 18, p. 253–558 (1983).MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • J. A. Pereira da Silva
    • 1
  1. 1.Departamento de MatemáticaUniversidade de CoimbraPortugal

Personalised recommendations