### 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 |
---|---|

Pages (from-to) | 171-180 |

Number of pages | 10 |

Journal | Letters in Mathematical Physics |

Volume | 46 |

Issue number | 2 |

Publication status | Published - 1998 Oct 2 |

Externally published | Yes |

### Fingerprint

### Keywords

- Deformation quantization
- Poisson algebra

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Letters in Mathematical Physics*,

*46*(2), 171-180.

**Deformation Quantizations of the Poisson Algebra of Laurent Polynomials.** / Omori, Hideki; Maeda, Yoshiaki; Miyazaki, Naoya; Yoshioka, Akira.

Research output: Contribution to journal › Article

*Letters in Mathematical Physics*, vol. 46, no. 2, pp. 171-180.

}

TY - JOUR

T1 - Deformation Quantizations of the Poisson Algebra of Laurent Polynomials

AU - Omori, Hideki

AU - Maeda, Yoshiaki

AU - Miyazaki, Naoya

AU - Yoshioka, Akira

PY - 1998/10/2

Y1 - 1998/10/2

N2 - It is well known that the Moyal bracket gives a unique deformation quantization of the canonical phase space ℝ2n 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.

AB - It is well known that the Moyal bracket gives a unique deformation quantization of the canonical phase space ℝ2n 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.

KW - Deformation quantization

KW - Poisson algebra

UR - http://www.scopus.com/inward/record.url?scp=0042403405&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042403405&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0042403405

VL - 46

SP - 171

EP - 180

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 2

ER -