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Double Poisson algebras
Author(s):
Michel
Van den Bergh
Journal:
Trans. Amer. Math. Soc.
360
(2008),
5711-5769.
MSC (2000):
Primary 53D30
Posted:
June 5, 2008
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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
Email:
michel.vandenbergh@uhasselt.be
DOI:
10.1090/S0002-9947-08-04518-2
PII:
S 0002-9947(08)04518-2
Keywords:
Non-commutative geometry,
p{{oly-vector}} fields,
Schouten bracket
Received by editor(s):
March 30, 2006
Posted:
June 5, 2008
Additional Notes:
The author is a senior researcher at the FWO
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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