POISSON DIXMIER–MOEGLIN EQUIVALENCE FROM A TOPOLOGICAL POINT OF VIEW
POISSON DIXMIER–MOEGLIN EQUIVALENCE FROM A TOPOLOGICAL POINT OF VIEW
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拓扑学角度的 POISSON DIXMIER–MOEGLIN 等价
DOI：
10.1007/s11856-021-2154-9
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发表时间：
2021
期刊：
影响因子：
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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
一个复仿射泊松代数满足泊松Dixmier-Moeglin等价，如果最大理想的泊松核恰好是在泊松素数谱中局部封闭的那些泊松素数理想，而且这些泊松素数理想恰好是其扩展泊松中心恰好是复数的那些泊松素数。本文给出了拟合集（P.specA,）的ain项及其最大谱上的辛叶或核层的Poisson Dixmier-Moeglin等价的一些拓扑判据。特别地，我们证明了泊松素数谱和每一个辛叶或辛核的Zariski拓扑可以检测任何复仿射泊松代数的泊松Dixmier-Moeglin等价。此外，我们推广了在[J]中证明的复仿射泊松代数的弱版泊松Dixmier-Moeglin等价。贝尔，S. Launois， O. L. Sánchez和B. Moosa，基于模型理论和微分代数几何的泊松代数，J. Eur。数学。Soc。[j] .中国科学（自然科学版）19(2017),2019-2049]。
A complex affine Poisson algebraAis said to satisfy the Poisson Dixmier-Moeglin equivalence if the Poisson cores of maximal ideals ofAare precisely those Poisson prime ideals that are locally closed in the Poisson prime spectrum P.specAand 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 forAin terms of the poset (P.specA, ⊆) 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. Sánchez 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.