On the geometric quantization of Poisson manifolds

In a paper by Huebschmann J. Reine Angew. Math. 408, 57 (1990), the geometric quantization of Poisson manifolds appears as a particular case of the quantization of Poisson algebras. Here, this quantization is presented straightforwardly. The results include a geometric prequantization integrality condition and its discussion in particular cases such as Dirac brackets, an adaptation of the notion of a polarization and a construction of a quantum Hilbert space, and a computational example. In the last section of the paper the general prequantization representations in the sense of Urwin Adv. Math. 50, 126 (1983) are described for the Poisson and Jacobi manifolds.