论文标题
非交通性衍生泊松减少
Noncommutative derived Poisson reduction
论文作者
论文摘要
在本文中，我们以Kontsevich-Rosenberg原则的精神提出了一个非交换性衍生的泊松式减少的程序：“某种$ a $上的非交换结构应在所有方案上提供类似的交换结构，$ {\ mathrm {rep}} _ n（a）_ n（a）$ {我们将双泊松结构用作非公共泊松结构和非公共性汉密尔顿空间（由M. van den Bergh首次介绍）来定义汉密尔顿动作的零基因座，以及非公共性的雪佛兰 - 埃伦贝格（Chevalley-Eilenberg）和BRST构造，显示了我们如何使用相应的代表性构建功能来恢复相应的构造。在专门的最终简短部分中，我们强调了表示形式的分类属性如何导致自然引入新有趣的概念，例如非交互性群体计划，小组行动或泊松组方案，这可以帮助以不同的眼光理解先前的结果，并将未来的研究概括为更广泛的，更加清晰的非等效性之间的相应性。
In this paper we propose a procedure for a noncommutative derived Poisson reduction, in the spirit of the Kontsevich-Rosenberg principle: "a noncommutative structure of some kind on $A$ should give an analogous commutative structure on all schemes ${\mathrm{Rep}}_n(A)$". We use double Poisson structures as noncommutative Poisson structures and noncommutative Hamiltonian spaces -- as first introduced by M. Van den Bergh -- to define (derived) zero loci of Hamiltonian actions and a noncommutative Chevalley-Eilenberg and BRST constructions, showing how we recover the corresponding commutative constructions using the representation functor. In a dedicated final short section we highlight how the categorical properties of the representation functor lead to the natural introduction of new interesting notions, such as noncommutative group schemes, group actions, or Poisson-group schemes, which could help to understand the previous results in a different light, and in future research generalise them into a broader, clearer correspondence between noncommutative and commutative equivariant geometry.
