Abstract
We describe a deformation quantization of a modification of Poisson geometry by a closed 3-form. Under suitable conditions, it gives rise to a stack of algebras. The basic object used for this aim is a kind of families of Poisson structures given by a Maurer–Cartan equation; they are easily quantized using Kontsevich's formality theorem. We conclude with a section on quantization of complex manifolds.
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Ševera, P. Quantization of Poisson Families and of Twisted Poisson Structures. Letters in Mathematical Physics 63, 105–113 (2003). https://doi.org/10.1023/A:1023077126186
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DOI: https://doi.org/10.1023/A:1023077126186