On the stratification of noncommutative prime spectra

Abstract

We study rational actions of an algebraic torus G G by automorphisms on an associative algebra R R . The G G -action on R R induces a stratification of the prime spectrum Spec ⁡ R \operatorname {Spec} R which was introduced by Goodearl and Letzter. For a noetherian algebra R R , Goodearl and Letzter showed that the strata of Spec ⁡ R \operatorname {Spec} 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 R .