On the stratification of noncommutative prime spectra

@article{Lorenz2012OnTS,
  title={On the stratification of noncommutative prime spectra},
  author={Martin Lorenz},
  journal={arXiv: Rings and Algebras},
  year={2012}
}
  • M. Lorenz
  • Published 31 May 2012
  • Mathematics
  • arXiv: Rings and Algebras
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 of R which was introduced by Goodearl and Letzter. For a noetherian algebra R, Goodearl and Letzter showed that the strata of the spectrum of 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. 
3 Citations
Hopf Algebra Actions and Rational Ideals
This note discusses a framework for the investigation of the prime spectrum of an associative algebra A that is equipped with an action of a Hopf algebra H . In particular, we study a notion of H
Actions of cocommutative Hopf algebras
Let $H$ be a cocommutative Hopf algebra acting on an algebra $A$. Assuming the base field to be algebraically closed and the $H$-action on $A$ to be integral, that is, it is given by a coaction of
On the importance of being primitive
  • J. Bell
  • Philosophy, Mathematics
  • 2019
espanolHacemos un breve estudio de la primitividad en la teoria de anillos y, en particular, veremos caracterizaciones de ideales primitivos en el espectro primo para varias clases de anillos.

References

SHOWING 1-10 OF 12 REFERENCES
Algebraic group actions on noncommutative spectra
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 set Spec R of all prime ideals of R,
Group actions and rational ideals
We develop the theory of rational ideals for arbitrary associative algebras R without assuming the standard finiteness conditions, noetherianness or the Goldie property. The Amitsur-Martindale ring
Prime spectra of quantized coordinate rings
This paper is partly a report on current knowledge concerning the structure of (generic) quantized coordinate rings and their prime spectra, and partly propaganda in support of the conjecture that
Lectures on Algebraic Quantum Groups
This book consists of an expanded set of lectures on algebraic aspects of quantum groups, concentrating particularly on quantized coordinate rings of algebraic groups and spaces and on quantized
The graded version of Goldie's Theorem
The analogue of Goldie's Theorem for prime rings is proved for rings graded by abelian groups, eliminating unnecessary additional hypotheses used in earlier versions.
The Dixmier-moeglin Equivalence in Quantum Coordinate Rings and Quantized Weyl Algebras
We study prime and primitive ideals in a uniied setting applicable to quanti-zations (at nonroots of unity) of n n matrices, of Weyl algebras, and of Euclidean and symplectic space. The framework for
Goodearl,Prime spectra of quantized coordinate rings , Interactions between ring theory and representations of a lgebras (Murcia)
  • Lecture Notes in Pure and Appl. Math., vol. 210,
  • 2000
Group actions and rational ideals, Algebra Number Theory
  • Transform. Groups
  • 2008
Brown and Ken R . Goodearl , Lectures on algebraic quantum groups , Advanced Courses in Mathematics . CRM Barcelona , Birkhäuser Verlag , Basel ,
  • 2002
Goodearl, Lectures on algebraic quantum groups
  • Advanced Courses in Mathematics. CRM Barcelona, Birkhäuser Verlag, Basel,
  • 2002
...
1
2
...