Classical lifting processes and multiplicative vector fields

Quarterly Journal of Mathematics

Volumn 49, Issue 193, 1998, Pages 59-85

  Mackenzie, Kirill C H ^a   Xu, Ping ^b  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032376689     PISSN: 00335606     EISSN: None     Source Type: Journal    
DOI: 10.1093/qjmath/49.193.59     Document Type: Article

References (20)

1. R. Abraham and J. Marsden, Foundations of Mechanics, 2nd edn, Addison-Wesley, Reading. Mau. (1985).
2. A. L. Besse, Manifolds all of whose Geodesics are Closed, Vol. 93 of Ergebnisse des Mathematik und ihrer Grenzgebiete. Springer-Verlag, Berlin (1978).
3. A. Coste, P. Dazord and A. Weinstein, 'Groupoïdes symplectiques'. In Publications du Département de Mathématiques de l'Université de Lyon, I, No. 2/A-1987, (1987), 1-65.
4. T. J. Courant, 'Dirac manifolds'. Trans. Amer. Math. Soc., 319 (1990) 631-661.
5. P. Dazord and D. Sondaz, 'Variétés de Poisson - Algébroïdes de Lie', Séminaire Sud-Rhodanien, 1988, Université Claude Bernard, Lyon I (1988), 1-68.
6. J. Dieudonné, Treatise on Analysis, Vol. 4. Academic Press, New York (1976).
7. M. Golubitsky and V. Guillemin, Stable Mappings and their Singularities, Graduate Texts in Mathematics, Vol. 14 Springer, New York (1973).
8. P. J. Higgins and K. C. H. Mackenzie, 'Algebraic constructions in the category of Lie algebroids'. J. Algebra, 129 (1990) 194-230.
9. P. Libermann and C.-M. Marle, Symplectic Geometry and Analytical Mechanics, Mathematics and its Applications D. Reidel, (1987).
10. J.-H. Lu and A. Weinstein, 'Poisson Lie groups, dressing transformations, and Bruhat decompositions'. J. Differential Geom. 31 (1990) 501-526.
11. K. Mackenzie, Lie Groupoids and Lie Algebroids in Differential Geometry. London Mathematical Society Lecture Note Series, No. 124, Cambridge University Press, Cambridge (1987).
12. K. C. H. Mackenzie, 'Double Lie algebroids and second-order geometry', I., Adv. Math. 94 (1992) 180-239.
13. K. C. H. Mackenzie, 'The calculus of vertical and complete lifts, and fields and forms on Lie algebroids and their duals', Journées Mathématiques et Informatique, No. 4, Université de Picardie, (1992-93) 30-49.
14. K. C. H. Mackenzie and Ping Xu, 'Lie bialgebroids and Poisson groupoids', Duke Math. J. 73 (1994) 415-452.
15. K. C. H. Mackenzie and Ping Xu, 'Integrability of Lie bialgebroids', Preprint (1996).
16. J. Pradines, 'Remarque sur le groupoïde cotangent de Weinstein-Dazord', C. R. Acad. Sci. Paris Sér. I Math. 306 (1988) 557-560.
17. A. Weinstein, Coisotropic calculus and Poisson groupoids.', J. Math. Soc. Japan 40 (1988) 705-727.
18. A. Weinstein, 'Affine Poisson structures', Internat. J. Math. 1 (1990) 343-360.
19. Ping Xu, 'On Poisson groupoids', Internat. J. Math. 6 (1995) 101-124.
20. K. Yano and S. Ishihara, Tangent and Cotangent Bundles, Vol. 16 of Pure and Applied Mathematics, Marcel Dekker, Inc., New York (1973).