### Abstract

It is well known that the Moyal bracket gives a unique deformation quantization of the canonical phase space ℝ^{2n} up to equivalence. In his presentation of an interesting deformation quantization of the Poisson algebra of Laurent polynomials, Ovsienko discusses the equivalences of deformation quantizations of these algebras. We show that under suitable conditions, deformation quantizations of this algebra are equivalent. Though Ovsienko showed that there exists a deformation quantization of the Poisson algebra of Laurent polynomials which is not equivalent to the Moyal product, this is not correct. We show this equivalence by two methods: a direct construction of the intertwiner via the star exponential and a more standard approach using Hochschild 2-cocycles.

Original language | English |
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Pages (from-to) | 171-180 |

Number of pages | 10 |

Journal | Letters in Mathematical Physics |

Volume | 46 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1998 Oct 2 |

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### Keywords

- Deformation quantization
- Poisson algebra

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Letters in Mathematical Physics*,

*46*(2), 171-180. https://doi.org/10.1023/A:1007521113652