Deformation quantizations of the Poisson algebra of Laurent polynomials (Q1282057)

It is proved that under certain conditions deformation quantizations of the canonical phase space \(\mathbb{R}^{2n}\) and the Poisson algebra of Laurent polynomials with the help of Moyal brackets are equivalent. The authors refute a previously accepted result that there exists a deformation quantization of the Poisson algebra of Laurent polynomials which is not equivalent to the Moyal product. The authors use two methods to get the results: A direct construction of the intertwiner via the star exponential and a more standard approach using Hochschild \(\alpha\)-cocycles.