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On the stratification of noncommutative prime spectra


Author: Martin Lorenz
Journal: Proc. Amer. Math. Soc. 142 (2014), 3013-3017
MSC (2010): Primary 16W22, 17B37, 20G42
DOI: https://doi.org/10.1090/S0002-9939-2014-12051-X
Published electronically: May 28, 2014
MathSciNet review: 3223357
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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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Additional Information

Martin Lorenz
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
Email: lorenz@temple.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12051-X
Keywords: Algebraic group, rational action, algebraic torus, rational ideal, prime spectrum, stratification
Received by editor(s): June 5, 2012
Received by editor(s) in revised form: September 26, 2012
Published electronically: May 28, 2014
Additional Notes: The research of the author was supported in part by NSA Grant H98230-12-1-0221
Communicated by: Binge Huisgen-Zimmermann
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.