Morita Equivalence of Formal Poisson Structures

Abstract We extend the notion of Morita equivalence Poisson manifolds to setting formal structures, that is, power series bivector fields $\pi =\pi _0 + \lambda \pi _1 +\cdots $ satisfying integrability condition $[\pi ,\pi ]=0$. Our main result gives a complete description equivalent structures deforming zero structure ($\pi _0=0$) in terms $B$-field transformations, relying on general study deformations morphisms and dual pairs. Combined with previous work star products [ 5], our results link notions geometry noncommutative algebra via deformation quantization.