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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An obstruction to quantizing compact symplectic manifolds
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by Mark J. Gotay, Janusz Grabowski and Hendrik B. Grundling PDF
Proc. Amer. Math. Soc. 128 (2000), 237-243 Request permission

Abstract:

We prove that there are no nontrivial finite-dimensional Lie representations of certain Poisson algebras of polynomials on a compact symplectic manifold. This result is used to establish the existence of a universal obstruction to quantizing a compact symplectic manifold, regardless of the dimensionality of the representation.
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Additional Information
  • Mark J. Gotay
  • Affiliation: Department of Mathematics, University of Hawaii, 2565 The Mall, Honolulu, Hawaii 96822
  • Email: gotay@math.hawaii.edu
  • Janusz Grabowski
  • Affiliation: Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland
  • Email: Janusz.Grabowski@mimuw.edu.pl
  • Hendrik B. Grundling
  • Affiliation: Department of Pure Mathematics, University of New South Wales, P.O. Box 1, Kensington, New South Wales, 2033 Australia
  • Email: hendrik@maths.unsw.edu.au
  • Received by editor(s): March 11, 1998
  • Published electronically: May 20, 1999
  • Communicated by: Peter Li
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 128 (2000), 237-243
  • MSC (1991): Primary 81S99; Secondary 17B66
  • DOI: https://doi.org/10.1090/S0002-9939-99-05007-8
  • MathSciNet review: 1622742