Download PDF - Linearization and star productsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Linearization and star products

Authors 1

Affiliations

  1. Département de mathématiques, Université de Metz, Ile du Saulcy, F-57045 Metz Cedex, France

Abstract

The aim of this paper is to give an overview concerning the problem of linearization of Poisson structures, more precisely we give results concerning Poisson-Lie groups and we apply those cohomological techniques to star products.

Bibliography

  1. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Deformation theory and quantization, Lett. Math. Phys. 1 (1977), 521-530.
  2. M. Bertelson, M. Cahen and S. Gutt, Equivalence of star products. Geometry and physics, Class. Quantum Grav. 14 (1997), A93-A107.
  3. V. Chloup-Arnould, Groupes de Lie-Poisson, Thèse de l'université de Metz (1996).
  4. V. Chloup-Arnould, Linearization of some Poisson-Lie tensor, J. of Geometry and Physics 24 (1997), 46-52.
  5. V. Chloup-Arnould, Star products on the algebra of polynomials on the dual of a semi-simple Lie algebra, Acad. Roy. Belg. Bull. Cl. Sci. (6) 8 (1997), no. 7-12, 263-269.
  6. M. Cahen, S. Gutt and J. Rawnsley, Non linearizability of the Iwasawa Poisson-Lie structure, Lett. Math. Phys. 24 (1992), 79-83.
  7. J. F. Conn, Normal forms for analytic Poisson structures, Ann. of Math. 119 (1984), 577-601.
  8. J. F. Conn, Normal forms for smooth Poisson structures, Ann. of Math. 121 (1985), 565-593.
  9. V. G. Drinfeld, Hamiltonian structure on Lie groups and the geometric meaning of the classical Yang-Baxter equation, Sov. Math. Dokl. 27 (1) (1983), 68-71.
  10. J. P. Dufour, Linéarisation de certaines structures de Poisson, J. Differential Geometry 32 (5) (1990), 415-428.
  11. S. Gutt, On the second Hochschild cohomology spaces for algebras of functions on a manifold, L.M.P. 39 (1997), 157-162.
  12. M. Kontsevich, Deformation quantization of Poisson manifold, I, q-alg 9709040.
  13. Molinier, Linéarisation de structures de Poisson, thèse de l'université de Montpellier II (1993).
  14. H. Omori, Y. Maeda and A. Yoshioka, Deformation quantizations of Poisson algebras, Contemp. Math. AMS 179 (1994), 213-240.
  15. A. Weinstein, The local structure of Poisson manifolds, J. Differential Geometry 18 (1983), 523-557.
  16. A. Weinstein, Poisson geometry of the principal series and non linearizable structures, J. Differential Geometry 25 (1987), 55-73.
Banach Center Publications
2000/51/1
Export to PBN, Opens in new tab
Pages:
55-60
Main language of publication
English
Published
2000
Exact and natural sciences