Advanced Search
Article Contents
Article Contents

Symmetries and reduction of multiplicative 2-forms

Abstract Related Papers Cited by
  • 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.
    Mathematics Subject Classification: Primary: 53D17.


    \begin{equation} \\ \end{equation}
  • [1]

    C. Arias Abad and M. Crainic, The Weil algebra and the Van Est isomorphism, Ann. Inst. Fourier, 61 (2011), 927-970.


    H. Bursztyn and A. Cabrera, Multiplicative forms at the infinitesimal level, Math. Annalen, 353 (2012), 663-705.


    H. Bursztyn, A. Cabrera and C. Ortiz, Linear and multiplicative 2-forms, Lett. Math. Phys., 90 (2009), 59-83.doi: 10.1007/s11005-009-0349-9.


    H. Bursztyn, G. Cavalcanti and M. Gualtieri, Reduction of Courant algebroids and generalized complex structures, Advances in Math., 211 (2007), 726-765.doi: 10.1016/j.aim.2006.09.008.


    H. Bursztyn, M. Crainic, A. Weinstein and C. Zhu, Integration of twisted Dirac brackets, Duke Math. J., 123 (2004), 549-607.doi: 10.1215/S0012-7094-04-12335-8.


    A. Cattaneo and G. Felder, Poisson sigma models and symplectic groupoids, in "Quantization of Singular Symplectic Quotients," Progr. Math., 198, Birkhäuser, Basel, (2001), 61-93.


    A. Coste, P. Dazord and A. Weinstein, Groupoïdes symplectiques, 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.


    T. Courant, Dirac manifolds, Trans. Amer. Math. Soc., 319 (1990), 631-661.doi: 10.1090/S0002-9947-1990-0998124-1.


    M. Crainic and R. Fernandes, Integrability of Lie brackets, Ann.of Math. (2), 157 (2003), 575-620.doi: 10.4007/annals.2003.157.575.


    M. Crainic and R. Fernandes, Integrability of Poisson brackets, J. Differential Geom., 66 (2004), 71-137.


    R. Fernandes, J.-P. Ortega and T. Ratiu, The momentum map in Poisson geometry, Amer. J. of Math., 131 (2009), 1261-1310doi: 10.1353/ajm.0.0068.


    M. Jotz and T. Ratiu, Induced Dirac structures on isotropy type manifolds, Transform. Groups, 16 (2011), 175-191.doi: 10.1007/s00031-011-9123-z.


    M. Jotz, T. Ratiu and J. Sniatycki, Singular reduction of Dirac structures, Trans. Amer. Math. Soc., 363 (2011), 2967-3013.doi: 10.1090/S0002-9947-2011-05220-7.


    K. Mackenzie and P. Xu, Classical lifting processes and multiplicative vector fields, Quart. J. Math. Oxford Ser. (2), 49 (1998), 59-85.


    K. Mackenzie and P. Xu, Integration of Lie bialgebroids, Topology, 39 (2000), 445-467.doi: 10.1016/S0040-9383(98)00069-X.


    K. Mikami and A. Weinstein, Moments and reduction for symplectic groupoids, Publ. Res. Inst. Math. Sci., 24 (1988), 121-140.doi: 10.2977/prims/1195175328.


    I. Moerdijk and J. Mrcun, On the integrability of Lie subalgebroids, Adv. Math., 204 (2006), 101-115.doi: 10.1016/j.aim.2005.05.011.


    P. Ševera, Some title containing the words "homotopy'' and"symplectic'', e.g. this one, in "Travaux Mathématiques. Fasc. XVI," Trav. Math., XVI, Univ. Luxemb., Luxembourg, (2005), 121-137.


    A. Weinstein, Symplectic groupoids and Poisson manifolds, Bull. Amer. Math. Soc. (N.S.), 16 (1987), 101-104.

  • 加载中

Article Metrics

HTML views() PDF downloads(176) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint