Ore extensions and Poisson algebras

TL;DR

This paper establishes a correspondence between the prime spectra of Ore extensions and Poisson prime spectra of polynomial algebras, providing insights into their structural similarities and differences.

Contribution

It introduces a homeomorphism linking prime spectra of Ore extensions and Poisson algebras, expanding understanding of their algebraic and geometric properties.

Findings

Homeomorphism between prime spectra of Ore extensions and Poisson algebras.

Examples including cases where A is d-simple.

Insights into the structure of Poisson and Ore extensions.

Abstract

For a derivation d of a commutative Noetherian complex algebra A, a homeomorphism is established between the prime spectrum of the Ore extension A[z;d] and the Poisson prime spectrum of the polynomial algebra A[z] endowed with the Poisson bracket such that {A,A}=0 and {z,a}=d(a) for all a in A. Several illustrative examples are discussed including some where A is known to be d-simple.