论文标题
双（准）泊松代数和可集成系统的动作角度二元性的形态
Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systems
论文作者
论文摘要
范登·伯格（Van Den Bergh）引入了双重（准）泊松代数，作为赋予（Quasi-）泊松支架的代数的非共同类似物。在这项工作中，我们提供了对双重（Quasi）泊松代数的形态学的研究，我们与Crawley-Boevey的$ H_0 $ -Poisson结构有关。我们特别证明，由van den bergh定义的双重（准）泊松代数结构，仅取决于被视为无向图的颤动，直到同构。我们从结果中得出了几种经典集成系统的动作角度二元性的表示理论描述。
Double (quasi-)Poisson algebras were introduced by Van den Bergh as non-commutative analogues of algebras endowed with a (quasi-)Poisson bracket. In this work, we provide a study of morphisms of double (quasi-)Poisson algebras, which we relate to the $H_0$-Poisson structures of Crawley-Boevey. We prove in particular that the double (quasi-)Poisson algebra structure defined by Van den Bergh for an arbitrary quiver only depends upon the quiver seen as an undirected graph, up to isomorphism. We derive from our results a representation theoretic description of action-angle duality for several classical integrable systems.
