Graded geometry and Poisson reduction

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Cattaneo, Alberto S.; Zambon, Marco; (2010)
  • Publisher: American Institute of Physics
  • Related identifiers: doi: 10.5167/uzh-28731, doi: 10.1063/1.3089207
  • Subject: Mathematics - Symplectic Geometry | 510 Mathematics | Institute of Mathematics | 53D17, 58A50 | Mathematics - Differential Geometry
    arxiv: Mathematics::Symplectic Geometry

The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternativ... View more
  • References (6)

    [1] H. Bursztyn, A. S. Cattaneo, R. Mehta, and M. Zambon. Generalized reduction via graded geometry, in preparation.

    [2] A. S. Cattaneo and M. Zambon. A supergeometric approach to Poisson reduction, Arxiv:1009.0948.

    [3] F. Falceto and M. Zambon. An extension of the Marsden-Ratiu reduction for Poisson manifolds, Lett. Math. Physics Vol. 85 (2008), pp. 203-219.

    [4] J. E. Marsden and T. Ratiu. Reduction of Poisson manifolds. Lett. Math. Phys., 11(2):161- 169, 1986.

    [5] D. Roytenberg. On the structure of graded symplectic supermanifolds and Courant algebroids. In Quantization, Poisson brackets and beyond (Manchester, 2001), volume 315 of Contemp. Math., pp. 169-185. Amer. Math. Soc., Providence, RI, 2002.

    [6] S. Waldmann. Poisson-Geometrie und Deformationsquantisierung. Eine Einfu¨hrung. Springer-Verlag Heidelberg, Berlin, New York, 2007. Institut fu¨r Mathematik, Universita¨t Zu¨rich-Irchel, Winterthurerstr. 190, CH-8057 Zu¨rich, Switzerland E-mail address: alberto.cattaneo@math.uzh.ch

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