Morita equivalence of formal Poisson structures

• Main Authors: Bursztyn, Henrique, Ortiz, Inocencio, Waldmann, Stefan
• Format: Journal Article
• Language: English
• Published: 17-06-2020
• Subjects: Mathematics - Symplectic Geometry
• DOI: 10.48550/arxiv.2006.10240

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 $\pi=\pi_0 + \lambda\pi_1 +\cdots$ 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, our results
link the notions of Morita equivalence in Poisson geometry and noncommutative
algebra via deformation quantization.