On the stratification of noncommutative prime spectra

TL;DR

This paper provides a new proof for the stratification of the prime spectrum of associative algebras under torus actions, extending previous results to a broader class of algebras.

Contribution

It introduces a generalized proof of the stratification of prime spectra under rational torus actions applicable to all associative algebras, not just noetherian ones.

Findings

Stratification of prime spectra is isomorphic to spectra of Laurent polynomial algebras.

The new proof applies to arbitrary associative algebras.

Extends previous results beyond noetherian cases.

Abstract

We study rational actions of an algebraic torus G by automorphisms on an associative algebra R. The G-action on R induces a stratification of the prime spectrum of R which was introduced by Goodearl and Letzter. For a noetherian algebra R, Goodearl and Letzter showed that the strata of the spectrum of R are isomorphic to the spectra of certain commutative Laurent polynomial algebras. The purpose of this note is to give a new proof of this result which works for arbitrary algebras R.