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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Double Poisson algebras
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by Michel Van den Bergh PDF
Trans. Amer. Math. Soc. 360 (2008), 5711-5769 Request permission

Abstract:

In this paper we develop Poisson geometry for non-commutative algebras. This generalizes the bi-symplectic geometry which was recently, and independently, introduced by Crawley-Boevey, Etingof and Ginzburg.

Our (quasi-)Poisson brackets induce classical (quasi-)Poisson brackets on representation spaces. As an application we show that the moduli spaces of representations associated to the deformed multiplicative preprojective algebras recently introduced by Crawley-Boevey and Shaw carry a natural Poisson structure.

References
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Additional Information
  • Michel Van den Bergh
  • Affiliation: Departement WNI, Limburgs Universitair Centrum, 3590 Diepenbeek, Belgium
  • MR Author ID: 176980
  • Email: michel.vandenbergh@uhasselt.be
  • Received by editor(s): March 30, 2006
  • Published electronically: June 5, 2008
  • Additional Notes: The author is a senior researcher at the FWO
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 5711-5769
  • MSC (2000): Primary 53D30
  • DOI: https://doi.org/10.1090/S0002-9947-08-04518-2
  • MathSciNet review: 2425689