Goodearl, Ken and Launois, Stephane
(2011)
*The Dixmier-Moeglin equivalence and a Gel'fand-Kirillov problem for Poisson polynomial algebras.*
Bulletin de la Société Mathématique de France , 139
(1).
pp. 1-39.
ISSN 0037-9484.
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Official URL http://smf4.emath.fr/en/Publications/Bulletin/139/... |

## Abstract

The structure of Poisson polynomial algebras of the type obtained as semiclassical limits of quantized coordinate rings is investigated. Sufficient conditions for a rational Poisson action of a torus on such an algebra to leave only finitely many Poisson prime ideals invariant are obtained. Combined with previous work of the first-named author, this establishes the Poisson Dixmier-Moeglin equivalence for large classes of Poisson polynomial rings, including semiclassical limits of quantum matrices, quantum symplectic and euclidean spaces, quantum symmetric and antisymmetric matrices. For a similarly large class of Poisson polynomial rings, it is proved that the quotient field of the algebra (respectively, of any Poisson prime factor ring) is a rational function field F(x(1), ..., x(n)) over the base field (respectively, over an extension field of the base field) with {x(i),x(j)} = lambda(ij)x(i)x(j)for suitable scalars lambda(ij), thus establishing a quadratic Poisson version of the Gel'fand-Kirillov problem. Finally, partial solutions to the isomorphism problem for Poisson fields of the type just mentioned are obtained.

Item Type: | Article |
---|---|

Subjects: | Q Science > QA Mathematics (inc Computing science) |

Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Pure Mathematics |

Depositing User: | Stephane Launois |

Date Deposited: | 04 Jul 2011 15:20 |

Last Modified: | 28 May 2014 10:54 |

Resource URI: | https://kar.kent.ac.uk/id/eprint/28003 (The current URI for this page, for reference purposes) |

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