Poisson catenarity in Poisson nilpotent algebras

TL;DR

This paper proves that in Poisson nilpotent algebras, the structure of Poisson prime ideals forms a well-behaved chain, with all chains between two given primes having the same length, revealing a fundamental structural property.

Contribution

It establishes the catenarity of the Poisson prime spectrum in Poisson nilpotent algebras, a property previously unknown for these structures.

Findings

Poisson prime spectrum is catenary in Poisson nilpotent algebras

All saturated chains of Poisson prime ideals have the same length

Provides structural insight into Poisson nilpotent algebra spectra

Abstract

We prove that for the iterated Poisson polynomial rings known as Poisson nilpotent algebras (or Poisson-CGL extensions), the Poisson prime spectrum is catenary, i.e., all saturated chains of inclusions of Poisson prime ideals between any two given Poisson prime ideals have the same length.