The Universal Generating Function of Analytical Poisson Structures

The notion of generating functions of Poisson structures was first studied in [2]. They are special functions which induce, on open subsets of R, a Poisson structure together with the local symplectic groupoid integrating it. A universal generating function was provided in terms of a formal power series coming from Kontsevich star product. The present article proves that this universal generating function converges for analytical Poisson structures and compares the induced local symplectic groupoid with the phase space of Karasev–Maslov. A brief introduction to symplectic groupoids in the perspective of quantization is provided.