# 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)

 PDF Author's Accepted Manuscript Language: English Download (231kB) Preview Preview This file may not be suitable for users of assistive technology. Request an accessible format Official URLhttps://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 10.1007/s10468-019-09879-3 Poisson algebra, Semi-invariant theory, Poisson Dixmier–Moeglin equivalence Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science Lewis Topley 29 Apr 2019 08:58 UTC 16 Feb 2021 14:04 UTC https://kar.kent.ac.uk/id/eprint/73658 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-4701-4384