Table of Contents Author Guidelines Submit a Manuscript
International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 643605, 36 pages
http://dx.doi.org/10.1155/2010/643605
Research Article

Formal Lagrangian Operad

1Institut für Mathematik, Universität Zürich—Irchel, Winterthurerstraße 190, 8057 Zürich, Switzerland
2Department of Mathematics, Utrecht University, Budapestlaan 6, 3584 CD Utrecht, The Netherlands
3D-MATH, ETH-Zentrum, 8092 Zürich, Switzerland

Received 14 July 2010; Accepted 7 December 2010

Academic Editor: A. Zayed

Copyright © 2010 Alberto S. Cattaneo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Kontsevich, “Deformation quantization of Poisson manifolds,” Letters in Mathematical Physics, vol. 66, no. 3, pp. 157–216, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. A. S. Cattaneo, B. Dherin, and G. Felder, “Formal symplectic groupoid,” Communications in Mathematical Physics, vol. 253, no. 3, pp. 645–674, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. A. S. Cattaneo, “The Lagrangian operad,” http://www.math.unizh.ch/reports/05_05.pdf.
  4. B. Dherin, Star products and symplectic groupoids, Ph.D. thesis, ETH Zürich, 2004.
  5. E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration, vol. 31 of Springer Series in Computational Mathematics, Springer, Berlin, Germany, 2002.
  6. M. Markl, “Homotopy algebras are homotopy algebras,” Forum Mathematicum, vol. 16, no. 1, pp. 129–160, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. M. Markl, S. Shnider, and J. Stasheff, Operads in Algebra, Topology and Physics, vol. 96 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 2002.
  8. A. S. Cattaneo, B. Dherin, and A. Weinstein, “Symplectic microgeometry I: micromorphisms,” The Journal of Symplectic Geometry, vol. 8, no. 2, pp. 205–223, 2010. View at Google Scholar
  9. M. Gerstenhaber and A. A. Voronov, “Homotopy G-algebras and moduli space operad,” International Mathematics Research Notices, no. 3, pp. 141–153, 1995. View at Publisher · View at Google Scholar
  10. B. Dherin, “The universal generating function of analytical Poisson structures,” Letters in Mathematical Physicss, vol. 75, no. 2, pp. 129–149, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. M. Cahen, S. Gutt, and M. De Wilde, “Local cohomology of the algebra of C functions on a connected manifold,” Letters in Mathematical Physics, vol. 4, no. 3, pp. 157–167, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. A. Coste, P. Dazord, and A. Weinstein, Groupoïdes Symplectiques, vol. 2 of Nouvelle Série A, Département de Mathématiques de l’Université Claude-Bernard de Lyon, Lyon, France, 1987.
  13. M. V. Karasëv, “The Maslov quantization conditions in higher cohomology and analogs of notions developed in Lie theory for canonical fibre bundles of symplectic manifolds II,” Selecta Mathematica Sovietica, vol. 8, pp. 235–257, 1989. View at Google Scholar · View at Zentralblatt MATH
  14. S. Zakrzewski, “Quantum and classical pseudogroups. I. Union pseudogroups and their quantization,” Communications in Mathematical Physics, vol. 134, no. 2, pp. 347–370, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. A. V. Karabegov, “Formal symplectic groupoid of a deformation quantization,” Communications in Mathematical Physics, vol. 258, no. 1, pp. 223–256, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH