Algebraic group actions on noncommutative spectra
| dc.creator | Lorenz, Martin | |
| dc.date | 2008-09-30 | |
| dc.date | 2009-03-16 | |
| dc.date.accessioned | 2026-07-07T12:52:14Z | |
| dc.date.available | 2026-07-07T12:52:14Z | |
| dc.description | Let G be an affine algebraic group and let R be an associative algebra with a rational action of G by algebra automorphisms. We study the induced G-action on the spectrum Spec R of all prime ideals of R, viewed as a topological space with the Jacobson-Zariski topology, and on the subspace consisting of all rational ideals of R. Here, a prime ideal P of R is said to be rational if the extended centroid of R/P is equal to the base field. The main themes of the article are local closedness of G-orbits in Spec R and the so-called G-stratification of Spec R. This stratification plays a central role in the recent investigation of algebraic quantum groups, in particular in the work of Goodearl and Letzter. We describe the G-strata in terms of certain commutative spectra. Our principal results are based on prior work of Moeglin & Rentschler and Vonessen. We generalize the theory arbitrary associative algebras while also simplifying some of the earlier proofs. | |
| dc.description | 21 pages; minor revisions; to appear in Transformation Groups | |
| dc.identifier | https://arxiv.org/abs/0809.5205 | |
| dc.identifier | http://arxiv.org/abs/0809.5205 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223232 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Quantum Algebra | |
| dc.subject | 16W22; 16W35; 17B37 | |
| dc.title | Algebraic group actions on noncommutative spectra | |
| dc.type | text |