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Transactions of the American Mathematical Society

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



Double Poisson algebras

Author: Michel Van den Bergh
Journal: Trans. Amer. Math. Soc. 360 (2008), 5711-5769
MSC (2000): Primary 53D30
Published electronically: June 5, 2008
MathSciNet review: 2425689
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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

Keywords: Non-commutative geometry, p{{oly-vector}} fields, Schouten bracket
Received by editor(s): March 30, 2006
Published electronically: June 5, 2008
Additional Notes: The author is a senior researcher at the FWO
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.