On the stratification of noncommutative prime spectra

Lorenz, Martin

doi:10.1090/S0002-9939-2014-12051-X

On the stratification of noncommutative prime spectra
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Proc. Amer. Math. Soc. 142 (2014), 3013-3017 Request permission

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 $\operatorname {Spec} R$ which was introduced by Goodearl and Letzter. For a noetherian algebra $R$, Goodearl and Letzter showed that the strata of $\operatorname {Spec} R$ 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 $R$.

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