@article{ASENS_2003_4_36_3_403_0,
author = {Xu, Ping},
title = {Dirac submanifolds and {Poisson} involutions},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
pages = {403--430},
year = {2003},
publisher = {Elsevier},
volume = {Ser. 4, 36},
number = {3},
doi = {10.1016/S0012-9593(03)00013-2},
mrnumber = {1977824},
zbl = {1047.53052},
language = {en},
url = {https://www.numdam.org/articles/10.1016/S0012-9593(03)00013-2/}
}
TY - JOUR AU - Xu, Ping TI - Dirac submanifolds and Poisson involutions JO - Annales scientifiques de l'École Normale Supérieure PY - 2003 SP - 403 EP - 430 VL - 36 IS - 3 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/S0012-9593(03)00013-2/ DO - 10.1016/S0012-9593(03)00013-2 LA - en ID - ASENS_2003_4_36_3_403_0 ER -
%0 Journal Article %A Xu, Ping %T Dirac submanifolds and Poisson involutions %J Annales scientifiques de l'École Normale Supérieure %D 2003 %P 403-430 %V 36 %N 3 %I Elsevier %U https://www.numdam.org/articles/10.1016/S0012-9593(03)00013-2/ %R 10.1016/S0012-9593(03)00013-2 %G en %F ASENS_2003_4_36_3_403_0
Xu, Ping. Dirac submanifolds and Poisson involutions. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 36 (2003) no. 3, pp. 403-430. doi: 10.1016/S0012-9593(03)00013-2
[1] , , Équation de Yang-Baxter dynamique classique et algébroïdes de Lie, C. R. Acad. Sci. Paris, Série I 327 (1998) 541-546. | Zbl | MR
[2] , Stokes matrices, Poisson Lie groups and Frobenius manifolds, Invent. Math. 146 (2001) 479-506. | Zbl | MR
[3] Bondal A., A symplectic groupoid of triangular bilinear forms and the braid group, Preprint, 1999.
[4] Bondal A., Symplectic groupoids related to Poisson-Lie groups, Preprint, 1999. | MR
[5] , , Geometric Models for Noncommutative Algebras, Berkeley Mathematics Lecture Notes, 10, American Mathematical Society, Providence, RI, 1999. | Zbl | MR
[6] , Dirac manifolds, Trans. Amer. Math. Soc. 319 (1990) 631-661. | Zbl | MR
[7] , Differentiable and algebroid cohomology, van Est isomorphisms, and characteristic classes, math.DG/0008064.
[8] , Lectures in Quantum Mechanics, Yeshiva University, 1964.
[9] , Dirac Structures and Integrability of Nonlinear Evolution Equations, Wiley, Chichester, 1993. | Zbl | MR
[10] , On Poisson homogeneous spaces of Poisson-Lie groups, Theoret. Math. Phys. 95 (1993) 524-525. | Zbl | MR
[11] , Geometry of 2D topological field theories, in: Integrable Systems and Quantum Groups, Lecture Notes in Math., 1620, Springer, Berlin, 1996, pp. 120-348. | Zbl | MR
[12] , , Geometry and classification of solutions of the classical dynamical Yang-Baxter equation, Comm. Math. Phys. 192 (1998) 77-120. | Zbl | MR
[13] , Conformal field theory and integrable systems associated to elliptic curves, in: Proc. ICM Zürich, 1994, pp. 1247-1255. | Zbl | MR
[14] Fernandes R., Completely integrable bi-Hamiltonian systems, Ph.D. Thesis, University of Minnesota, 1994. | MR
[15] , A note on Poisson symmetric spaces, in: Proceeding of the Cornelius Lanczos International Centenary Conference, 1994, pp. 638-642.
[16] , Connections in Poisson geometry I: Holonomy and invariants, J. Differential Geom. 54 (2000) 303-365. | Zbl | MR
[17] , , Hyperelliptic Prym varieties and integrable systems, Comm. Math. Phys. 221 (2001) 169-196. | Zbl | MR
[18] , , Lie-Poisson structure on some Poisson Lie groups, J. Amer. Math. Soc. 5 (1992) 445-453. | Zbl | MR
[19] , , On dynamical Poisson groupoids I, math.DG/0209212.
[20] , , , Manin triples for Lie bialgebroids, J. Differential Geom. 45 (1997) 547-574. | Zbl | MR
[21] , , , Dirac structures and Poisson homogeneous spaces, Comm. Math. Phys. 192 (1998) 121-144. | Zbl | MR
[22] , , Exact Lie bialgebroids and Poisson groupoids, Geom. Funct. Anal. 6 (1996) 138-145. | Zbl | MR
[23] , , Dirac structures and dynamical r-matrices, Ann. Inst. Fourier 51 (2001) 831-859. | Zbl | MR | Numdam
[24] , Momentum mappings and reduction of Poisson actions, in: Symplectic Geometry, Groupoids, and Integrable Systems, MSRI Publ., 20, Springer, New York, 1991, pp. 209-226. | Zbl | MR
[25] , , Poisson Lie groups, dressing transformations, and Bruhat decompositions, J. Differential Geom. 31 (1990) 501-526. | Zbl | MR
[26] , , Groupoïdes symplectiques doubles des groupes de Lie-Poisson, C. R. Acad. Sci. Paris, Série I 309 (1989) 951-954. | Zbl | MR
[27] , , Lie bialgebroids and Poisson groupoids, Duke Math. J. 18 (1994) 415-452. | Zbl | MR
[28] , , Integration of Lie bialgebroids, Topology 39 (2000) 445-467. | Zbl | MR
[29] , , Reduction of Poisson manifolds, Lett. Math. Phys. 11 (1986) 161-169. | Zbl | MR
[30] , Structure transverse aux orbites de la représentation coadjointe : le cas des orbites réductives, Sém. Géom. Diff. USTL (Montpellier) (1984) 55-62. | Zbl
[31] , , The Bruhat order on symmetric varieties, Geom. Dedicata 35 (1990) 389-436. | Zbl | MR
[32] , Some results on algebraic groups with involutions, Adv. Stud. Pure Math. 6 (1985) 525-543. | Zbl | MR
[33] , On a Poisson structure on the space of Stokes matrices, Internat. Math. Res. Notices 9 (1999) 473-493. | Zbl | MR
[34] , The local structure of Poisson manifolds, J. Differential Geom. 18 (1983) 523-557. | Zbl | MR
[35] , Symplectic groupoids and Poisson manifolds, Bull. Amer. Math. Soc. (N.S.) 16 (1987) 101-104. | Zbl | MR
[36] , The modular automorphism group of a Poisson manifold, J. Geom. Phys. 23 (1997) 379-394. | Zbl | MR
[37] , Symplectic groupoids of reduced Poisson spaces, C. R. Acad. Sci. Paris, Série I 314 (1992) 457-461. | Zbl | MR
[38] , On Poisson groupoids, Internat. J. Math. 6 (1995) 101-124. | Zbl | MR
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