On the stratification of noncommutative prime spectra

Lorenz, Martin

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

On the stratification of noncommutative prime spectra
HTML articles powered by AMS MathViewer

by Martin Lorenz

Proc. Amer. Math. Soc. 142 (2014), 3013-3017

DOI: https://doi.org/10.1090/S0002-9939-2014-12051-X

Published electronically: May 28, 2014

PDF | 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 $R$.

References

Ken A. Brown and Ken R. Goodearl, Lectures on algebraic quantum groups, Advanced Courses in Mathematics. CRM Barcelona, Birkhäuser Verlag, Basel, 2002. MR 1898492, DOI 10.1007/978-3-0348-8205-7
K. R. Goodearl, Prime spectra of quantized coordinate rings, Interactions between ring theory and representations of algebras (Murcia), Lecture Notes in Pure and Appl. Math., vol. 210, Dekker, New York, 2000, pp. 205–237. MR 1759846
K. R. Goodearl and E. S. Letzter, The Dixmier-Moeglin equivalence in quantum coordinate rings and quantized Weyl algebras, Trans. Amer. Math. Soc. 352 (2000), no. 3, 1381–1403. MR 1615971, DOI 10.1090/S0002-9947-99-02345-4
K. R. Goodearl and J. T. Stafford, The graded version of Goldie’s theorem, Algebra and its applications (Athens, OH, 1999) Contemp. Math., vol. 259, Amer. Math. Soc., Providence, RI, 2000, pp. 237–240. MR 1780524, DOI 10.1090/conm/259/04098
Martin Lorenz, Group actions and rational ideals, Algebra Number Theory 2 (2008), no. 4, 467–499. MR 2411408, DOI 10.2140/ant.2008.2.467
Martin Lorenz, Algebraic group actions on noncommutative spectra, Transform. Groups 14 (2009), no. 3, 649–675. MR 2534802, DOI 10.1007/s00031-009-9059-8