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Foreword
Symmetries and reduction of multiplicative 2-forms
1. | Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, 22460-320, Brazil |
2. | Departamento de Matemática Aplicada, Instituto de Matemática, Universidade Federal do Rio de Janeiro, CEP 21941-909, Rio de Janeiro - RJ, Brazil |
References:
[1] |
C. Arias Abad and M. Crainic, The Weil algebra and the Van Est isomorphism,, Ann. Inst. Fourier, 61 (2011), 927. Google Scholar |
[2] |
H. Bursztyn and A. Cabrera, Multiplicative forms at the infinitesimal level,, Math. Annalen, 353 (2012), 663. Google Scholar |
[3] |
H. Bursztyn, A. Cabrera and C. Ortiz, Linear and multiplicative 2-forms,, Lett. Math. Phys., 90 (2009), 59.
doi: 10.1007/s11005-009-0349-9. |
[4] |
H. Bursztyn, G. Cavalcanti and M. Gualtieri, Reduction of Courant algebroids and generalized complex structures,, Advances in Math., 211 (2007), 726.
doi: 10.1016/j.aim.2006.09.008. |
[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] |
A. Cattaneo and G. Felder, Poisson sigma models and symplectic groupoids,, in, 198 (2001), 61.
|
[7] |
A. Coste, P. Dazord and A. Weinstein, Groupoïdes symplectiques,, in, 87-2 (1987), 87.
|
[8] |
T. Courant, Dirac manifolds,, Trans. Amer. Math. Soc., 319 (1990), 631.
doi: 10.1090/S0002-9947-1990-0998124-1. |
[9] |
M. Crainic and R. Fernandes, Integrability of Lie brackets,, Ann.of Math. (2), 157 (2003), 575.
doi: 10.4007/annals.2003.157.575. |
[10] |
M. Crainic and R. Fernandes, Integrability of Poisson brackets,, J. Differential Geom., 66 (2004), 71.
|
[11] |
R. Fernandes, J.-P. Ortega and T. Ratiu, The momentum map in Poisson geometry,, Amer. J. of Math., 131 (2009), 1261.
doi: 10.1353/ajm.0.0068. |
[12] |
M. Jotz and T. Ratiu, Induced Dirac structures on isotropy type manifolds,, Transform. Groups, 16 (2011), 175.
doi: 10.1007/s00031-011-9123-z. |
[13] |
M. Jotz, T. Ratiu and J. Sniatycki, Singular reduction of Dirac structures,, Trans. Amer. Math. Soc., 363 (2011), 2967.
doi: 10.1090/S0002-9947-2011-05220-7. |
[14] |
, J.-H. Lu,, private communication., (). Google Scholar |
[15] |
K. Mackenzie and P. Xu, Classical lifting processes and multiplicative vector fields,, Quart. J. Math. Oxford Ser. (2), 49 (1998), 59.
|
[16] |
K. Mackenzie and P. Xu, Integration of Lie bialgebroids,, Topology, 39 (2000), 445.
doi: 10.1016/S0040-9383(98)00069-X. |
[17] |
K. Mikami and A. Weinstein, Moments and reduction for symplectic groupoids,, Publ. Res. Inst. Math. Sci., 24 (1988), 121.
doi: 10.2977/prims/1195175328. |
[18] |
I. Moerdijk and J. Mrcun, On the integrability of Lie subalgebroids,, Adv. Math., 204 (2006), 101.
doi: 10.1016/j.aim.2005.05.011. |
[19] |
P. Ševera, Some title containing the words "homotopy'' and"symplectic'', e.g. this one,, in, (2005), 121.
|
[20] |
A. Weinstein, Symplectic groupoids and Poisson manifolds,, Bull. Amer. Math. Soc. (N.S.), 16 (1987), 101.
|
show all references
References:
[1] |
C. Arias Abad and M. Crainic, The Weil algebra and the Van Est isomorphism,, Ann. Inst. Fourier, 61 (2011), 927. Google Scholar |
[2] |
H. Bursztyn and A. Cabrera, Multiplicative forms at the infinitesimal level,, Math. Annalen, 353 (2012), 663. Google Scholar |
[3] |
H. Bursztyn, A. Cabrera and C. Ortiz, Linear and multiplicative 2-forms,, Lett. Math. Phys., 90 (2009), 59.
doi: 10.1007/s11005-009-0349-9. |
[4] |
H. Bursztyn, G. Cavalcanti and M. Gualtieri, Reduction of Courant algebroids and generalized complex structures,, Advances in Math., 211 (2007), 726.
doi: 10.1016/j.aim.2006.09.008. |
[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] |
A. Cattaneo and G. Felder, Poisson sigma models and symplectic groupoids,, in, 198 (2001), 61.
|
[7] |
A. Coste, P. Dazord and A. Weinstein, Groupoïdes symplectiques,, in, 87-2 (1987), 87.
|
[8] |
T. Courant, Dirac manifolds,, Trans. Amer. Math. Soc., 319 (1990), 631.
doi: 10.1090/S0002-9947-1990-0998124-1. |
[9] |
M. Crainic and R. Fernandes, Integrability of Lie brackets,, Ann.of Math. (2), 157 (2003), 575.
doi: 10.4007/annals.2003.157.575. |
[10] |
M. Crainic and R. Fernandes, Integrability of Poisson brackets,, J. Differential Geom., 66 (2004), 71.
|
[11] |
R. Fernandes, J.-P. Ortega and T. Ratiu, The momentum map in Poisson geometry,, Amer. J. of Math., 131 (2009), 1261.
doi: 10.1353/ajm.0.0068. |
[12] |
M. Jotz and T. Ratiu, Induced Dirac structures on isotropy type manifolds,, Transform. Groups, 16 (2011), 175.
doi: 10.1007/s00031-011-9123-z. |
[13] |
M. Jotz, T. Ratiu and J. Sniatycki, Singular reduction of Dirac structures,, Trans. Amer. Math. Soc., 363 (2011), 2967.
doi: 10.1090/S0002-9947-2011-05220-7. |
[14] |
, J.-H. Lu,, private communication., (). Google Scholar |
[15] |
K. Mackenzie and P. Xu, Classical lifting processes and multiplicative vector fields,, Quart. J. Math. Oxford Ser. (2), 49 (1998), 59.
|
[16] |
K. Mackenzie and P. Xu, Integration of Lie bialgebroids,, Topology, 39 (2000), 445.
doi: 10.1016/S0040-9383(98)00069-X. |
[17] |
K. Mikami and A. Weinstein, Moments and reduction for symplectic groupoids,, Publ. Res. Inst. Math. Sci., 24 (1988), 121.
doi: 10.2977/prims/1195175328. |
[18] |
I. Moerdijk and J. Mrcun, On the integrability of Lie subalgebroids,, Adv. Math., 204 (2006), 101.
doi: 10.1016/j.aim.2005.05.011. |
[19] |
P. Ševera, Some title containing the words "homotopy'' and"symplectic'', e.g. this one,, in, (2005), 121.
|
[20] |
A. Weinstein, Symplectic groupoids and Poisson manifolds,, Bull. Amer. Math. Soc. (N.S.), 16 (1987), 101.
|
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