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Poisson spectra in polynomial algebras. (English) Zbl 1351.17023

Summary: A significant class of Poisson brackets on the polynomial algebra \(\mathbb C[x_1,\dots ,x_n]\) 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.

MSC:

17B63 Poisson algebras
16S36 Ordinary and skew polynomial rings and semigroup rings

Software:

Macaulay2
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References:

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