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 |
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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 |
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| DOI/Identification number: | 10.1007/s10468-019-09879-3 |
| Uncontrolled keywords: | Poisson algebra, Semi-invariant theory, Poisson Dixmier–Moeglin equivalence |
| Divisions: | 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: | 05 Nov 2024 12:36 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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| CReDIT Contributor Roles: |
Topley, Lewis.
| Creator's ORCID: |
 https://orcid.org/0000-0002-4701-4384
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