June  2012, 4(2): 111-127. doi: 10.3934/jgm.2012.4.111

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

Received  March 2011 Revised  July 2011 Published  August 2012

This paper is concerned with symmetries of closed multiplicative 2-forms on Lie groupoids and their infinitesimal counterparts. We use them to study Lie group actions on Dirac manifolds by Dirac diffeomorphisms and their lifts to presymplectic groupoids, building on recent work of Fernandes-Ortega-Ratiu [11] on Poisson actions.
Citation: Henrique Bursztyn, Alejandro Cabrera. Symmetries and reduction of multiplicative 2-forms. Journal of Geometric Mechanics, 2012, 4 (2) : 111-127. doi: 10.3934/jgm.2012.4.111
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show all references

References:
[1]

Ann. Inst. Fourier, 61 (2011), 927-970. Google Scholar

[2]

Math. Annalen, 353 (2012), 663-705. Google Scholar

[3]

Lett. Math. Phys., 90 (2009), 59-83. doi: 10.1007/s11005-009-0349-9.  Google Scholar

[4]

Advances in Math., 211 (2007), 726-765. doi: 10.1016/j.aim.2006.09.008.  Google Scholar

[5]

Duke Math. J., 123 (2004), 549-607. doi: 10.1215/S0012-7094-04-12335-8.  Google Scholar

[6]

in "Quantization of Singular Symplectic Quotients," Progr. Math., 198, Birkhäuser, Basel, (2001), 61-93.  Google Scholar

[7]

in "Publications du Département de Mathématiques. Nouvelle Série. A," Vol. 2, Publ. Dép. Math. Nouvelle Sér. A, 87-2, Univ. Claude-Bernard, Lyon, (1987), i-ii, 1-62.  Google Scholar

[8]

Trans. Amer. Math. Soc., 319 (1990), 631-661. doi: 10.1090/S0002-9947-1990-0998124-1.  Google Scholar

[9]

Ann.of Math. (2), 157 (2003), 575-620. doi: 10.4007/annals.2003.157.575.  Google Scholar

[10]

J. Differential Geom., 66 (2004), 71-137.  Google Scholar

[11]

Amer. J. of Math., 131 (2009), 1261-1310 doi: 10.1353/ajm.0.0068.  Google Scholar

[12]

Transform. Groups, 16 (2011), 175-191. doi: 10.1007/s00031-011-9123-z.  Google Scholar

[13]

Trans. Amer. Math. Soc., 363 (2011), 2967-3013. doi: 10.1090/S0002-9947-2011-05220-7.  Google Scholar

[14]

, J.-H. Lu,, private communication., ().   Google Scholar

[15]

Quart. J. Math. Oxford Ser. (2), 49 (1998), 59-85.  Google Scholar

[16]

Topology, 39 (2000), 445-467. doi: 10.1016/S0040-9383(98)00069-X.  Google Scholar

[17]

Publ. Res. Inst. Math. Sci., 24 (1988), 121-140. doi: 10.2977/prims/1195175328.  Google Scholar

[18]

Adv. Math., 204 (2006), 101-115. doi: 10.1016/j.aim.2005.05.011.  Google Scholar

[19]

in "Travaux Mathématiques. Fasc. XVI," Trav. Math., XVI, Univ. Luxemb., Luxembourg, (2005), 121-137.  Google Scholar

[20]

Bull. Amer. Math. Soc. (N.S.), 16 (1987), 101-104.  Google Scholar

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