On the Semi-centre of a Poisson Algebra

Lecoutre, Cesar, Topley, Lewis (2019) On the Semi-centre of a Poisson Algebra. Algebras and Representation Theory, 23 . pp. 875-886. ISSN 1386-923X. (doi:10.1007/s10468-019-09879-3) (KAR id:73658)

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Official URL: https://doi.org/10.1007/s10468-019-09879-3

Abstract

If g is a Lie algebra then the semi-centre of the Poisson algebra S(g) is the subalgebra generated by ad(g) -eigenvectors. In this paper we abstract this definition to the context of integral Poisson algebras. We identify necessary and sufficient conditions for the Poisson semi-centre Asc to be a Poisson algebra graded by its weight spaces. In that situation we show the Poisson semi-centre exhibits many nice properties: the rational Casimirs are quotients of Poisson normal elements and the Poisson Dixmier–Mœglin equivalence holds for Asc.

Item Type:	Article
DOI/Identification number:	10.1007/s10468-019-09879-3
Uncontrolled keywords:	Poisson algebra, Semi-invariant theory, Poisson Dixmier–Moeglin equivalence
Institutional Unit:	Schools > School of Engineering, Mathematics and Physics > Mathematical Sciences
Former Institutional Unit:	Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User:	Lewis Topley
Date Deposited:	29 Apr 2019 08:58 UTC
Last Modified:	20 May 2025 11:39 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/73658 (The current URI for this page, for reference purposes)

University of Kent Author Information

Lecoutre, Cesar.

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Topley, Lewis.

Creator's ORCID:	https://orcid.org/0000-0002-4701-4384
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