no. 3
Dirac submanifolds and Poisson involutions
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 36 (2003) no. 3, pp. 403-430. 
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     author = {Xu, Ping},
     title = {Dirac submanifolds and {Poisson} involutions},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {403--430},
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     volume = {Ser. 4, 36},
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     year = {2003},
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     zbl = {1047.53052},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S0012-9593(03)00013-2/}
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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. http://www.numdam.org/articles/10.1016/S0012-9593(03)00013-2/

[1] Bangoura M., Kosmann-Schwarzbach Y., Équation de Yang-Baxter dynamique classique et algébroïdes de Lie, C. R. Acad. Sci. Paris, Série I 327 (1998) 541-546. | MR | Zbl

[2] Boalch P., Stokes matrices, Poisson Lie groups and Frobenius manifolds, Invent. Math. 146 (2001) 479-506. | MR | Zbl

[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] Cannas Da Silva A., Weinstein A., Geometric Models for Noncommutative Algebras, Berkeley Mathematics Lecture Notes, 10, American Mathematical Society, Providence, RI, 1999. | MR | Zbl

[6] Courant T.J., Dirac manifolds, Trans. Amer. Math. Soc. 319 (1990) 631-661. | MR | Zbl

[7] Crainic M., Differentiable and algebroid cohomology, van Est isomorphisms, and characteristic classes, math.DG/0008064.

[8] Dirac P.A.M., Lectures in Quantum Mechanics, Yeshiva University, 1964.

[9] Dorfman I., Dirac Structures and Integrability of Nonlinear Evolution Equations, Wiley, Chichester, 1993. | MR | Zbl

[10] Drinfel'D V.G., On Poisson homogeneous spaces of Poisson-Lie groups, Theoret. Math. Phys. 95 (1993) 524-525. | MR | Zbl

[11] Dubrovin B., Geometry of 2D topological field theories, in: Integrable Systems and Quantum Groups, Lecture Notes in Math., 1620, Springer, Berlin, 1996, pp. 120-348. | MR | Zbl

[12] Etingof P., Varchenko A., Geometry and classification of solutions of the classical dynamical Yang-Baxter equation, Comm. Math. Phys. 192 (1998) 77-120. | MR | Zbl

[13] Felder G., Conformal field theory and integrable systems associated to elliptic curves, in: Proc. ICM Zürich, 1994, pp. 1247-1255. | MR | Zbl

[14] Fernandes R., Completely integrable bi-Hamiltonian systems, Ph.D. Thesis, University of Minnesota, 1994. | MR

[15] Fernandes R., A note on Poisson symmetric spaces, in: Proceeding of the Cornelius Lanczos International Centenary Conference, 1994, pp. 638-642.

[16] Fernandes R., Connections in Poisson geometry I: Holonomy and invariants, J. Differential Geom. 54 (2000) 303-365. | MR | Zbl

[17] Fernandes R., Vanhaecke P., Hyperelliptic Prym varieties and integrable systems, Comm. Math. Phys. 221 (2001) 169-196. | MR | Zbl

[18] Ginzburg V., Weinstein A., Lie-Poisson structure on some Poisson Lie groups, J. Amer. Math. Soc. 5 (1992) 445-453. | MR | Zbl

[19] Li L.-C., Parmentier S., On dynamical Poisson groupoids I, math.DG/0209212.

[20] Liu Z.-J., Weinstein A., Xu P., Manin triples for Lie bialgebroids, J. Differential Geom. 45 (1997) 547-574. | MR | Zbl

[21] Liu Z.-J., Weinstein A., Xu P., Dirac structures and Poisson homogeneous spaces, Comm. Math. Phys. 192 (1998) 121-144. | MR | Zbl

[22] Liu Z.-J., Xu P., Exact Lie bialgebroids and Poisson groupoids, Geom. Funct. Anal. 6 (1996) 138-145. | MR | Zbl

[23] Liu Z.-J., Xu P., Dirac structures and dynamical r-matrices, Ann. Inst. Fourier 51 (2001) 831-859. | Numdam | MR | Zbl

[24] Lu J.H., Momentum mappings and reduction of Poisson actions, in: Symplectic Geometry, Groupoids, and Integrable Systems, MSRI Publ., 20, Springer, New York, 1991, pp. 209-226. | MR | Zbl

[25] Lu J.H., Weinstein A., Poisson Lie groups, dressing transformations, and Bruhat decompositions, J. Differential Geom. 31 (1990) 501-526. | MR | Zbl

[26] Lu J.H., Weinstein A., Groupoïdes symplectiques doubles des groupes de Lie-Poisson, C. R. Acad. Sci. Paris, Série I 309 (1989) 951-954. | MR | Zbl

[27] Mackenzie K., Xu P., Lie bialgebroids and Poisson groupoids, Duke Math. J. 18 (1994) 415-452. | MR | Zbl

[28] Mackenzie K., Xu P., Integration of Lie bialgebroids, Topology 39 (2000) 445-467. | MR | Zbl

[29] Marsden J., Ratiu T., Reduction of Poisson manifolds, Lett. Math. Phys. 11 (1986) 161-169. | MR | Zbl

[30] Molino P., Structure transverse aux orbites de la représentation coadjointe : le cas des orbites réductives, Sém. Géom. Diff. USTL (Montpellier) (1984) 55-62. | Zbl

[31] Richardson R.W., Springer T.A., The Bruhat order on symmetric varieties, Geom. Dedicata 35 (1990) 389-436. | MR | Zbl

[32] Springer T.A., Some results on algebraic groups with involutions, Adv. Stud. Pure Math. 6 (1985) 525-543. | MR | Zbl

[33] Ugaglia M., On a Poisson structure on the space of Stokes matrices, Internat. Math. Res. Notices 9 (1999) 473-493. | MR | Zbl

[34] Weinstein A., The local structure of Poisson manifolds, J. Differential Geom. 18 (1983) 523-557. | MR | Zbl

[35] Weinstein A., Symplectic groupoids and Poisson manifolds, Bull. Amer. Math. Soc. (N.S.) 16 (1987) 101-104. | MR | Zbl

[36] Weinstein A., The modular automorphism group of a Poisson manifold, J. Geom. Phys. 23 (1997) 379-394. | MR | Zbl

[37] Xu P., Symplectic groupoids of reduced Poisson spaces, C. R. Acad. Sci. Paris, Série I 314 (1992) 457-461. | MR | Zbl

[38] Xu P., On Poisson groupoids, Internat. J. Math. 6 (1995) 101-124. | MR | Zbl

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