Double Poisson algebras
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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.
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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