Poisson spectra in polynomial algebras

A significant class of Poisson brackets on the polynomial algebra C[x1,…,xn] is studied and, for this class of Poisson brackets, the Poisson prime ideals, Poisson primitive ideals and symplectic cores are determined. Moreover it is established that these Poisson algebras satisfy the Poisson Dixmier–...

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Bibliographic Details
Published in:Journal of algebra 2014-02, Vol.400, p.56-71
Main Authors: Jordan, David A., Oh, Sei-Qwon
Format: Article
Language:English
Subjects:
Poisson algebra
Poisson prime ideal
Polynomial algebra
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Summary:A significant class of Poisson brackets on the polynomial algebra C[x1,…,xn] is studied and, for this class of Poisson brackets, the Poisson prime ideals, Poisson primitive ideals and symplectic cores are determined. Moreover it is established that these Poisson algebras satisfy the Poisson Dixmier–Moeglin equivalence.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2013.11.004