Linearization problems for Lie algebroids and Lie groupoids

Letters in Mathematical Physics

Volumn 52, Issue 1, 2000, Pages 93-102

  Weinstein, Alan ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Averaging; Group action; Invariant submanifold; Lie algebroid; Lie groupoid; Linearization; Poisson structure

Indexed keywords

EID: 0001994242     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007657920231     Document Type: Article

References (26)

1. Almeida, R. and Molino, P.: Suites d'Atiyah et feuilletages transversalement complets, C.R. Acad. Sci. Paris Sér. I Math. 300 (1985), 13-15.
2. Atiyah, M. F.: Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982), 1-15.
3. Bochner, S.: Compact groups of differentiable transformations, Ann. of Math. 46 (1945), 372-381.
4. Cannas da Silva, A. and Weinstein, A., Geometric Models for Noncommutative Algebras, Berkeley Math. Lecture Notes, Amer. Math. Soc., Providence, R.I., 1999.
5. Conn, J. F.: Normal forms for analytic Poisson structures, Ann. of Math. 119 (1984), 576-601.
6. Conn, J. F.: Normal forms for smooth Poisson structures, Ann. of Math. 121 (1985), 565-593.
7. Dazord, P.: Feuilletages à singularités, Nederl. Akad. Wetensch. Indag. Math. 47 (1985), 21-39.
8. de la Harpe, P. and Karoubi, M.: Représentations approchées d'un groupe dans une algèbre de Banach, Manuscripta Math. 22 (1977), 293-310.
9. ∞, Séminaire de géométrie, 1985-1986, Publ. Dép. Math. Nouvelle Sér. B, 86-4, Univ. Claude-Bernard, Lyon, 1986, pp. 55-68.
10. Flato, M. and Simon, J.: On a linearization program of nonlinear field equations, Phys. Lett. B 94 (1980), 518-522.
11. 1-close group actions. Math. Z. 132 (1973), 11-20.
12. Grove, K., Karcher, H., and Ruh, E. A.: Group actions and curvature, Invent. Math. 23 (1974), 31-48.
13. Guillemin, V. W. and Sternberg, S.: Remarks on a paper of Hermann, Trans. Amer. Math. Soc. 130 (1968), 110-116.
14. Guillemin, V. and Sternberg, S.: Convexity properties of the moment mapping, Invent. Math. 67 (1982), 491-513.
15. Guillemin, V. and Sternberg, S.: Convexity properties of the moment mapping II, Invent. Math. 77 (1984), 533-546.
16. Hermann, R.: The formal linearization of a semisimple Lie algebra of vector fields about a singular point, Trans. Amer. Math. Soc. 130 (1968), 105-109.
17. Kirwan, F.: Convexity properties of the moment mapping III, Invent. Math. 77 (1984), 547-552.
18. Kushnirenko, A. G.: Linear-equivalent action of a semisimple Lie group in the neighborhood of a fixed point, Funct. Anal. Appl. 1 (1967), 89-90.
19. Mackenzie, K.: Lie Groupoids and Lie Algebroids in Differential Geometry, London Math. Soc. Lecture Notes Ser. 124, Cambridge University Press, Cambridge, 1987.
20. Mikami, K. and Weinstein, A.: Moments and reduction for symplectic groupoids, Publ. Res. Inst. Math. Sci. 24 (1988), 121-140.
21. Ulam, S.: Sets, Numbers, and Universes: Selected Works, W. A. Beyer et al. (eds), The MIT Press, Cambridge, Mass., 1974.
22. Wade, A.: Normalisation formelle de structures de Poisson, C. R. Acad. Sci. Paris Sér. I Math. 324 (1997), 531-536.
23. Weinstein, A.: Lectures on Symplectic Manifolds, Regional Conf. Ser. Math. 29, Amer. Math. Soc., Providence, R.I., 1977.
24. Weinstein, A.: From Riemann geometry to Poisson geometry and back again, Lecture at Chern Symposium, MSRI, 1998, available at http://msri.org/publications/video/ contents.html.
25. Weinstein, A., Almost invariant submanifolds for compact group actions, J. Europ. Math. Soc. 2 (2000), 53-86.
26. Weinstein, A.: Proper groupoids (in preparation).