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On the Dixmier-Moeglin equivalence for Poisson-Hopf algebras

Launois, Stephane, Sanchez, Omar Leon (2019) On the Dixmier-Moeglin equivalence for Poisson-Hopf algebras. Advances in Mathematics, 346 . pp. 48-69. ISSN 0001-8708. E-ISSN 1090-2082. (doi:10.1016/j.aim.2019.01.036)

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Abstract

We prove that the Poisson version of the Dixmier-Moeglin equivalence

holds for cocommutative a?ne Poisson-Hopf algebras. This is a ?rst step

towards understanding the symplectic foliation and the representation theory

of (cocommutative) a?ne Poisson-Hopf algebras. Our proof makes substantial

use of the model theory of ?elds equipped with ?nitely many possibly noncommuting

derivations. As an application, we show that the symmetric algebra of

a ?nite dimensional Lie algebra, equipped with its natural Poisson structure,

satis?es the Poisson Dixmier-Moeglin equivalence.

Item Type: Article
DOI/Identification number: 10.1016/j.aim.2019.01.036
Uncontrolled keywords: Dixmier–Moeglin equivalence, Poisson–Hopf algebras, Model theory of differential fields
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Stephane Launois
Date Deposited: 21 Jan 2019 16:22 UTC
Last Modified: 23 Aug 2019 13:22 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/71755 (The current URI for this page, for reference purposes)
Launois, Stephane: https://orcid.org/0000-0001-7252-8515
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