Quantization of Whitney functions and reduction
M. J. Pflaum, H. Posthuma, and X. Tang
Journal of Singularities
volume 13 (2015), 217-228
Received 23 October 2013.
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Abstract:
For a possibly singular subset of a regular Poisson manifold we construct a deformation quantization of its algebra of Whitney functions. We then extend the construction of a deformation quantization to the case where the underlying set is a subset of a not necessarily regular Poisson manifold which can be written as the quotient of a regular Poisson manifold on which a compact Lie group acts freely by Poisson maps. Finally, if the quotient Poisson manifold is regular as well, we show a "quantization commutes with reduction" type result. For the proofs, we use methods stemming from both singularity theory and Poisson geometry.
Author(s) information:
Markus J. Pflaum | Hessel Posthuma | Xiang Tang |
Department of Mathematics | Korteweg-de Vries Institute for Mathematics | Department of Mathematics |
University of Colorado | University of Amsterdam | Washington University |
Boulder, USA | The Netherlands | St. Louis, USA |
email: markus.pflaum@colorado.edu | email: h.b.posthuma@uva.nl | email: xtang@math.wustl.edu |