The Dixmier-Moeglin equivalence and a Gel'fand-Kirillov problem for Poisson polynomial algebras

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. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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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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