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Morita Equivalence of Formal Poisson Structures
International Mathematics Research Notices ( IF 0.9 ) Pub Date : 2021-05-26 , DOI: 10.1093/imrn/rnab096
Henrique Bursztyn 1 , Inocencio Ortiz 2 , Stefan Waldmann 3
Affiliation  

We extend the notion of Morita equivalence of Poisson manifolds to the setting of formal Poisson structures, that is, formal power series of bivector fields $\pi =\pi _0 + \lambda \pi _1 +\cdots $ satisfying the Poisson integrability condition $[\pi ,\pi ]=0$. Our main result gives a complete description of Morita equivalent formal Poisson structures deforming the zero structure ($\pi _0=0$) 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 [ 5], our results link the notions of Morita equivalence in Poisson geometry and noncommutative algebra via deformation quantization.

中文翻译:

形式泊松结构的 Morita 等价性

我们将 Poisson 流形的 Morita 等价概念扩展到形式 Poisson 结构的设置,即满足 Poisson 可积性条件 $\pi =\pi _0 + \lambda \pi _1 +\cdots $ 的形式幂级数[\pi ,\pi ]=0$。我们的主要结果完整描述了 Morita 等价形式 Poisson 结构在 $B$ 场变换方面对零结构 ($\pi _0=0$) 进行变形,这依赖于对 Poisson 态射和对偶对的形式变形的一般研究. 结合之前关于星积 [5] 的 Morita 等价的工作,我们的结果通过变形量化将 Poisson 几何中的 Morita 等价概念与非交换代数联系起来。
更新日期:2021-05-26
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