POISSON DIXMIER–MOEGLIN EQUIVALENCE FROM A TOPOLOGICAL POINT OF VIEW
POISSON DIXMIER–MOEGLIN EQUIVALENCE FROM A TOPOLOGICAL POINT OF VIEW
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DOI：
10.1007/s11856-021-2154-9
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Quanshui Wu
中科院分区：
文献类型：
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作者：
Juan Luo;Xingting Wang;Quanshui Wu
A complex affine Poisson algebra A is said to satisfy the Poisson Dixmier–.Moeglin equivalence if the Poisson cores of maximal ideals of A are precisely.those Poisson prime ideals that are locally closed in the Poisson.prime spectrum P.specA and if, moreover, these Poisson prime ideals are.precisely those whose extended Poisson centers are exactly the complex.numbers..In this paper, we provide some topological criteria for the Poisson.Dixmier–Moeglin equivalence for A in terms of the poset (P.spec A,⊆) and.the symplectic leaf or core stratification on its maximal spectrum. In particular,.we prove that the Zariski topology of the Poisson prime spectrum.and of each symplectic leaf or core can detect the Poisson Dixmier–Moeglin.equivalence for any complex affine Poisson algebra. Moreover, we generalize.the weaker version of the Poisson Dixmier–Moeglin equivalence for a.complex affine Poisson algebra proved in [J. Bell, S. Launois, O. L. S´anchez.and B. Moosa, Poisson algebras via model theory and differential-algebraic.geometry, J. Eur. Math. Soc. (JEMS) 19 (2017), 2019–2049] to the general.context of a commutative differential algebra.
