论文标题
莫里塔等效的形式泊松结构
Morita equivalence of formal Poisson structures
论文作者
论文摘要
我们将Poisson歧管等效的概念扩展到{\ em正式}泊松结构的设置，即，bivector领域的形式功率系列$π=π_0 +λπ_1 + vis_1 + \ cdots $满足Poisson集成性条件$ [π，π] = 0 $。我们的主要结果对Morita等效的正式泊松结构进行了完整描述，这些结构在$ b $ field转换方面将零结构变形（$π_0= 0 $）变形，依赖于对泊松形态和二重对的形式变形的一般研究。结合先前关于恒星产品的莫里塔等效性的工作，我们的结果通过变形量化将莫里塔等效性的概念与非交通代数的概念联系起来。
We extend the notion of Morita equivalence of Poisson manifolds to the setting of {\em formal} Poisson structures, i.e., formal power series of bivector fields $π=π_0 + λπ_1 +\cdots$ satisfying the Poisson integrability condition $[π,π]=0$. Our main result gives a complete description of Morita equivalent formal Poisson structures deforming the zero structure ($π_0=0$) in terms of $B$-field transformations, relying on a general study of formal deformations of Poisson morphisms and dual pairs. Combined with previous work on Morita equivalence of star products, our results link the notions of Morita equivalence in Poisson geometry and noncommutative algebra via deformation quantization.
