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Volumn 39, Issue 3, 2000, Pages 445-467

Integration of Lie bialgebroids

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EID: 0034179182     PISSN: 00409383     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0040-9383(98)00069-X     Document Type: Article
Times cited : (120)

References (38)
  • 4
    • 38249009099 scopus 로고
    • Determination of a double Lie groupoid by its core diagram
    • [4] R. Brown, K.C.H. Mackenzie, Determination of a double Lie groupoid by its core diagram, Journal of Pure and Applied Algebra 80 (3) (1992) 237-272.
    • (1992) Journal of Pure and Applied Algebra , vol.80 , Issue.3 , pp. 237-272
    • Brown, R.1    Mackenzie, K.C.H.2
  • 5
    • 0000960526 scopus 로고
    • The monodromy groupoid of a Lie groupoid. Cahiers topologie et géom
    • [5] R. Brown, O. Mucuk, The monodromy groupoid of a Lie groupoid. Cahiers Topologie et Géom. Différentielle Catégoriques 36 (4) (1995) 345-369.
    • (1995) Différentielle Catégoriques , vol.36 , Issue.4 , pp. 345-369
    • Brown, R.1    Mucuk, O.2
  • 6
    • 0002722894 scopus 로고
    • Publications du Département de Mathématiques de l'Université de Lyon, I, 2/A-1987
    • [6] A. Coste, P. Dazord, A. Weinstein, Groupoïdes symplectiques, Publications du Département de Mathématiques de l'Université de Lyon, I, 2/A-1987 (1987) 1-65.
    • (1987) Groupoïdes Symplectiques , pp. 1-65
    • Coste, A.1    Dazord, P.2    Weinstein, A.3
  • 7
    • 0012099180 scopus 로고
    • Lie groups and lie algebras in infinite dimension: A new approach
    • Y. Maeda, H. Omori, A. Weinstein, eds. Symplectic Geometry and Quantization, July
    • [7] P. Dazord, Lie groups and Lie algebras in infinite dimension: A new approach. In: Y. Maeda, H. Omori, A. Weinstein, eds. Symplectic Geometry and Quantization, Contemporary Mathematics, Vol. 179. Amer. Math. Soc., July 1993, pp. 17-44.
    • (1993) Contemporary Mathematics, Vol. 179. Amer. Math. Soc. , vol.179 , pp. 17-44
    • Dazord, P.1
  • 9
    • 0002785466 scopus 로고
    • Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of the classical Yang-Baxter equation
    • [9] V.G. Drinfel'd, Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of the classical Yang-Baxter equation, Soviet Mathematics Dokledy 27 (1983) 68-71.
    • (1983) Soviet Mathematics Dokledy , vol.27 , pp. 68-71
    • Drinfel'd, V.G.1
  • 10
    • 0000855801 scopus 로고
    • Algebraic constructions in the category of Lie algebroids
    • [10] P.J. Higgins, K.C.H. Mackenzie, Algebraic constructions in the category of Lie algebroids, Jounal of Algebra 129 (1990) 194-230.
    • (1990) Jounal of Algebra , vol.129 , pp. 194-230
    • Higgins, P.J.1    Mackenzie, K.C.H.2
  • 11
    • 0000092620 scopus 로고
    • Analogues of objects of the theory of Lie groups for nonlinear poisson brackets
    • [11] M.V. Karasev, Analogues of objects of the theory of Lie groups for nonlinear Poisson brackets, Izvestiya Akademia Nauk SSSR Seriya Matematicheskaya 50 (1986) 508-538, 638, English translation: Mathematics of the USSR-Izvestiya 28 (3) (1987) 497-527.
    • (1986) Izvestiya Akademia Nauk SSSR Seriya Matematicheskaya , vol.50 , pp. 508-538
    • Karasev, M.V.1
  • 12
    • 0005215531 scopus 로고
    • [11] M.V. Karasev, Analogues of objects of the theory of Lie groups for nonlinear Poisson brackets, Izvestiya Akademia Nauk SSSR Seriya Matematicheskaya 50 (1986) 508-538, 638, English translation: Mathematics of the USSR-Izvestiya 28 (3) (1987) 497-527.
    • (1987) English Translation: Mathematics of the USSR-Izvestiya , vol.28 , Issue.3 , pp. 497-527
  • 13
    • 0002237617 scopus 로고
    • The Maslov quantization conditions in higher cohomology and analogs of notions developed in lie theory for canonical fibre bundles of symplectic manifolds. I, II
    • Preprint, Moscov. Inst. Electron Mashinostroeniya, 1981, deposited at VINITI, 1982
    • [12] M.V. Karasev, The Maslov quantization conditions in higher cohomology and analogs of notions developed in Lie theory for canonical fibre bundles of symplectic manifolds. I, II. Selecta Mathematica Sovietica 8 (1989) 213-234, 235-258, Preprint, Moscov. Inst. Electron Mashinostroeniya, 1981, deposited at VINITI, 1982.
    • (1989) Selecta Mathematica Sovietica , vol.8 , pp. 213-234
    • Karasev, M.V.1
  • 14
    • 0002257066 scopus 로고
    • Nonlinear poisson brackets: Geometry and quantization
    • American Mathematical Society, Providence, R.I.
    • [13] M.V. Karasev, V.P. Maslov, Nonlinear Poisson Brackets: Geometry and Quantization. Translations of Mathematical Monographs, vol. 119, American Mathematical Society, Providence, R.I., 1993.
    • (1993) Translations of Mathematical Monographs , vol.119
    • Karasev, M.V.1    Maslov, V.P.2
  • 15
    • 0001133433 scopus 로고
    • Exact Gerstenhaber algebras and Lie bialgebroids
    • [14] Y. Kosmann-Schwarzbach, Exact Gerstenhaber algebras and Lie bialgebroids, Acta Applicadae Mathematicae 41 (1995) 153-165.
    • (1995) Acta Applicadae Mathematicae , vol.41 , pp. 153-165
    • Kosmann-Schwarzbach, Y.1
  • 16
    • 0000572127 scopus 로고    scopus 로고
    • The Lie bialgebroid of a Poisson-Nijenhuis manifold
    • [15] Y. Kosmann-Schwarzbach, The Lie bialgebroid of a Poisson-Nijenhuis manifold. Letters in Mathematical Physics, 38 (1996) 421-428.
    • (1996) Letters in Mathematical Physics , vol.38 , pp. 421-428
    • Kosmann-Schwarzbach, Y.1
  • 19
    • 0003842982 scopus 로고
    • Zweiter Abschnitt, unter Mitwirkung von Prof. Dr. Friedrich Engel., Teubner, Leipzig
    • [18] S. Lie, Theorie der Transformationsgruppen. Zweiter Abschnitt, unter Mitwirkung von Prof. Dr. Friedrich Engel., Teubner, Leipzig, 1890.
    • (1890) Theorie Der Transformationsgruppen
    • Lie, S.1
  • 22
    • 0030550696 scopus 로고    scopus 로고
    • Exact Lie bialgebroids and Poisson groupoids
    • [21] Z.J. Liu, P. Xu, Exact Lie bialgebroids and Poisson groupoids. Geometry and Functional Analysis 6 (1996) 138-145.
    • (1996) Geometry and Functional Analysis , vol.6 , pp. 138-145
    • Liu, Z.J.1    Xu, P.2
  • 23
    • 84972494622 scopus 로고
    • Poisson Lie groups, dressing transformations, and bruhat decompositions
    • [22] J.-H. Lu, A. Weinstein, Poisson Lie groups, dressing transformations, and Bruhat decompositions, Journal of Differential Geometry 31 (1990) 501-526.
    • (1990) Journal of Differential Geometry , vol.31 , pp. 501-526
    • Lu, J.-H.1    Weinstein, A.2
  • 24
    • 0003276054 scopus 로고
    • Lie Groupoids and Lie Algebroids in Differential Geometry
    • Cambridge University Press, Cambridge
    • [23] K. Mackenzie, Lie Groupoids and Lie Algebroids in Differential Geometry. London Mathematical Society Lecture Note Series, Vol. 124. Cambridge University Press, Cambridge, 1987.
    • (1987) London Mathematical Society Lecture Note Series , vol.124
    • Mackenzie, K.1
  • 25
    • 0000636313 scopus 로고
    • Double Lie algebroids and second-order geometry, I
    • [24] K.C.H. Mackenzie, Double Lie algebroids and second-order geometry, I, Advances in Mathematics 94 (2) (1992) 180-239.
    • (1992) Advances in Mathematics , vol.94 , Issue.2 , pp. 180-239
    • Mackenzie, K.C.H.1
  • 27
    • 0033243236 scopus 로고    scopus 로고
    • On symplectic double groupoids and the duality of Poisson groupoids
    • to appear
    • [26] K.C.H. Mackenzie, On symplectic double groupoids and the duality of Poisson groupoids, International Journal of Mathematics 1999 (to appear).
    • (1999) International Journal of Mathematics
    • Mackenzie, K.C.H.1
  • 28
    • 84973999707 scopus 로고
    • Lie bialgebroids and Poisson groupoids
    • [27] K.C.H. Mackenzie, P. Xu, Lie bialgebroids and Poisson groupoids, Duke Mathematical Journal 73 (2) (1994) 415-452.
    • (1994) Duke Mathematical Journal , vol.73 , Issue.2 , pp. 415-452
    • Mackenzie, K.C.H.1    Xu, P.2
  • 29
    • 0032376689 scopus 로고    scopus 로고
    • Classical lifting processes and multiplicative vector fields
    • [28] K.C.H. Mackenzie, P. Xu, Classical lifting processes and multiplicative vector fields. Quarterly Journal of Mathematics Oxford (2) 49 (1998) 59-85.
    • (1998) Quarterly Journal of Mathematics Oxford , vol.49 , Issue.2 , pp. 59-85
    • Mackenzie, K.C.H.1    Xu, P.2
  • 30
    • 85037799176 scopus 로고    scopus 로고
    • On Lie algebroid actions and morphisms. Cahiers de topologie et géom
    • [29] T. Mokri, On Lie algebroid actions and morphisms. Cahiers de Topologie et Géom. Différentielle Catégoriques, 37 (1996) 315-331.
    • (1996) Différentielle Catégoriques , vol.37 , pp. 315-331
    • Mokri, T.1
  • 31
    • 0000041163 scopus 로고
    • Théorie de lie pour les groupoïdes différentiables. Relations entre propriétés locales et globales
    • [30] J. Pradines, Théorie de Lie pour les groupoïdes différentiables. Relations entre propriétés locales et globales, Comptes Rendus des Seances de l'Academie des Sciences Paris, Série A 263 (1966) 907-910.
    • (1966) Comptes Rendus des Seances de L'academie des Sciences Paris, Série A , vol.263 , pp. 907-910
    • Pradines, J.1
  • 34
    • 84972531238 scopus 로고
    • The local structure of Poisson manifolds
    • Errata and Addenda, 22 (1985) 255
    • [33] A. Weinstein, The local structure of Poisson manifolds, Journal of Differential Geometry 18 (1983) 523-557, Errata and Addenda, 22 (1985) 255.
    • (1983) Journal of Differential Geometry , vol.18 , pp. 523-557
    • Weinstein, A.1


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