Double Poisson algebras

被引：124
作者：
Van Den Bergh, Michel [1 ]
机构：
[1] Limburgs Univ Ctr, Dept WNI, B-3590 Diepenbeek, Belgium
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 360卷 / 11期
关键词：
non-commutative geometry; poly-vector fields; Schouten bracket;
D O I：
10.1090/S0002-9947-08-04518-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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收藏
页码：5711 / 5769
页数：59
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