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.