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Poisson and integrable systems through the Nambu bracket and its Jacobi multiplier
Picard group of isotropic realizations of twisted Poisson manifolds
1. | Department of Mathematics, Cornell University, Ithaca, NY 14853, United States |
References:
[1] |
A. Alekseev, H. Bursztyn and E. Meinrenken, Pure spinors on Lie groups,, in Asterique, 327 (2009), 131.
|
[2] |
A. Alekseev, A. Malkin and E. Meinrenken, Lie group valued moment maps,, J. Differential Geom., 48 (1998), 445.
|
[3] |
P. Balseiro and L. García-Naranjo, Gauge transformations, twisted Poisson brackets and Hamiltonianization of nonholonomic systems,, Arch. Rat. Mech. Anal., 205 (2012), 267.
doi: 10.1007/s00205-012-0512-9. |
[4] |
K. Behrend, P. Xu and B. Zhang, Equivariant gerbes over compact simple Lie groups,, C. R. Acad. Sci. Paris, 336 (2003), 251.
doi: 10.1016/S1631-073X(02)00024-9. |
[5] |
H. Bursztyn, M. Crainic, A. Weinstein and C. Zhu, Integration of twisted Dirac brackets,, Duke Math. J., 123 (2004), 549.
doi: 10.1215/S0012-7094-04-12335-8. |
[6] |
H. Bursztyn and A. Weinstein, Picard groups in Poisson geometry,, Moscow Math. J., 4 (2004), 39.
|
[7] |
A. Catteneo and P. Xu, Integration of twisted Poisson structures,, J. Geom. Phys., 49 (2004), 187.
doi: 10.1016/S0393-0440(03)00086-X. |
[8] |
M. Crainic and R. Fernandes, Integrability of Lie brackets,, Ann. of Math., 157 (2003), 575.
doi: 10.4007/annals.2003.157.575. |
[9] |
M. Crainic and R. Fernandes, Integrablity of Poisson brackets,, J. Differential Geom., 66 (2004), 71.
|
[10] |
P. Dazord and T. Delzant, Le problème général des variables actions-angles,, J. Differential Geom., 26 (1987), 223.
|
[11] |
H. Duan, Schubert calculus and cohomology of Lie groups. Part II. Compact Lie groups,, preprint, (). Google Scholar |
[12] |
J. J. Duistermaat, On global action-angle variables,, Comm. Pure Appl. Math., 33 (1980), 687.
doi: 10.1002/cpa.3160330602. |
[13] |
F. Fassò and N. Sansonetto, Integrable almost-symplectic Hamiltonian systems,, J. Math. Phys., 48 (2007).
doi: 10.1063/1.2783937. |
[14] |
K. Guruprasad, J. Huebschmann, L. Jeffrey and A. Weinstein, Group systems, groupoids, and moduli spaces of parabolic bundles,, Duke Math. J., 89 (1997), 377.
doi: 10.1215/S0012-7094-97-08917-1. |
[15] |
R. Hartshorne, Algebraic Geometry,, Graduate Text in Mathematics, 52 (1977).
|
[16] |
N. Sansonetto and D. Sepe, Twisted isotropic realizations of twisted Poisson structures,, J. Geometric Mechanics, 5 (2013), 233.
doi: 10.3934/jgm.2013.5.233. |
[17] |
P. Severa and A. Weinstein, Poisson geometry with a 3-form background,, in Noncommutative Geometry and String Theory (Yokohama, (2001), 145.
doi: 10.1143/PTPS.144.145. |
[18] |
R. Sjamaar, Hans Duistermaat's contributions to Poisson geometry,, Bull. Braz. Math. Soc., 42 (2011), 783.
doi: 10.1007/s00574-011-0035-2. |
[19] |
I. Vaisman, Lectures on the Geometry of Poisson Manifolds,, Progress in Mathematics, (1994).
doi: 10.1007/978-3-0348-8495-2. |
[20] |
P. Xu, Morita equivalent symplectic groupoids,, in Symplectic geometry, 20 (1991), 291.
doi: 10.1007/978-1-4613-9719-9_20. |
show all references
References:
[1] |
A. Alekseev, H. Bursztyn and E. Meinrenken, Pure spinors on Lie groups,, in Asterique, 327 (2009), 131.
|
[2] |
A. Alekseev, A. Malkin and E. Meinrenken, Lie group valued moment maps,, J. Differential Geom., 48 (1998), 445.
|
[3] |
P. Balseiro and L. García-Naranjo, Gauge transformations, twisted Poisson brackets and Hamiltonianization of nonholonomic systems,, Arch. Rat. Mech. Anal., 205 (2012), 267.
doi: 10.1007/s00205-012-0512-9. |
[4] |
K. Behrend, P. Xu and B. Zhang, Equivariant gerbes over compact simple Lie groups,, C. R. Acad. Sci. Paris, 336 (2003), 251.
doi: 10.1016/S1631-073X(02)00024-9. |
[5] |
H. Bursztyn, M. Crainic, A. Weinstein and C. Zhu, Integration of twisted Dirac brackets,, Duke Math. J., 123 (2004), 549.
doi: 10.1215/S0012-7094-04-12335-8. |
[6] |
H. Bursztyn and A. Weinstein, Picard groups in Poisson geometry,, Moscow Math. J., 4 (2004), 39.
|
[7] |
A. Catteneo and P. Xu, Integration of twisted Poisson structures,, J. Geom. Phys., 49 (2004), 187.
doi: 10.1016/S0393-0440(03)00086-X. |
[8] |
M. Crainic and R. Fernandes, Integrability of Lie brackets,, Ann. of Math., 157 (2003), 575.
doi: 10.4007/annals.2003.157.575. |
[9] |
M. Crainic and R. Fernandes, Integrablity of Poisson brackets,, J. Differential Geom., 66 (2004), 71.
|
[10] |
P. Dazord and T. Delzant, Le problème général des variables actions-angles,, J. Differential Geom., 26 (1987), 223.
|
[11] |
H. Duan, Schubert calculus and cohomology of Lie groups. Part II. Compact Lie groups,, preprint, (). Google Scholar |
[12] |
J. J. Duistermaat, On global action-angle variables,, Comm. Pure Appl. Math., 33 (1980), 687.
doi: 10.1002/cpa.3160330602. |
[13] |
F. Fassò and N. Sansonetto, Integrable almost-symplectic Hamiltonian systems,, J. Math. Phys., 48 (2007).
doi: 10.1063/1.2783937. |
[14] |
K. Guruprasad, J. Huebschmann, L. Jeffrey and A. Weinstein, Group systems, groupoids, and moduli spaces of parabolic bundles,, Duke Math. J., 89 (1997), 377.
doi: 10.1215/S0012-7094-97-08917-1. |
[15] |
R. Hartshorne, Algebraic Geometry,, Graduate Text in Mathematics, 52 (1977).
|
[16] |
N. Sansonetto and D. Sepe, Twisted isotropic realizations of twisted Poisson structures,, J. Geometric Mechanics, 5 (2013), 233.
doi: 10.3934/jgm.2013.5.233. |
[17] |
P. Severa and A. Weinstein, Poisson geometry with a 3-form background,, in Noncommutative Geometry and String Theory (Yokohama, (2001), 145.
doi: 10.1143/PTPS.144.145. |
[18] |
R. Sjamaar, Hans Duistermaat's contributions to Poisson geometry,, Bull. Braz. Math. Soc., 42 (2011), 783.
doi: 10.1007/s00574-011-0035-2. |
[19] |
I. Vaisman, Lectures on the Geometry of Poisson Manifolds,, Progress in Mathematics, (1994).
doi: 10.1007/978-3-0348-8495-2. |
[20] |
P. Xu, Morita equivalent symplectic groupoids,, in Symplectic geometry, 20 (1991), 291.
doi: 10.1007/978-1-4613-9719-9_20. |
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