Related papers: Quantized coordinate rings and related noetherian …

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 since these algebras share many common…

This is a survey of what is known and/or conjectured about the prime and primitive spectra of quantum algebras, of quantized coordinate rings in particular. The topological structure of these spectra, their relations to classical affine…

Given an affine algebraic variety V and a quantization A of its coordinate ring, it is conjectured that the primitive ideal space of A can be expressed as a topological quotient of V. Evidence in favor of this conjecture is discussed, and…

First some old as well as new results about P.I. algebras, Ore extensions, and degrees are presented. Then quantized $n\times r$ matrices as well as quantized factor algebras of $M_q(n)$ are analyzed. The latter are the quantized function…

This paper offers an expository account of some ideas, methods, and conjectures concerning quantized coordinate rings and their semiclassical limits, with a particular focus on primitive ideal spaces. The semiclassical limit of a family of…

For the algebra $A$ in the title, its prime, primitive and maximal spectra are classified. The group of automorphisms of $A$ is determined. The simple unfaithful $A$-modules and the simple weight $A$-modules are classified.

The aim of this paper is to study the representation theory of quantum Schubert cells. Let $\g$ be a simple complex Lie algebra. To each element $w$ of the Weyl group $W$ of $\g$, De Concini, Kac and Procesi have attached a subalgebra…

We describe the prime and primitive spectra for quantized enveloping algebras at roots of 1 in characteristic zero in terms of the prime spectrum of the underlying enveloping algebra. For primitive ideals we obtain an analogue of Duflo's…

We describe the Poisson ideals and attached symplectic geometry of a cluster algebra with compatible Poisson structure. We apply these results to determine the spectrum of a quantum cluster algebra. As an application, we describe the…

The main purpose of this paper is a wide generalization of one of the results abstract algebraic geometry begins with, namely of the fact that the prime spectrum $\mathrm{Spec}(R)$ of a unital commutative ring $R$ is always a spectral…

A framework is developed to describe the Zariski topologies on the prime and primitive spectra of a quantum algebra $A$ in terms of the (known) topologies on strata of these spaces and maps between the collections of closed sets of…

A quantum solvable algebra is an iterated $q$-skew extension of a commutative algebra. We get finite statification of prime spectrum for quantum solvable algebras obeying some natural conditions. We prove that for any prime ideal $I$ the…

Several topologies can be defined on the prime, the maximal and the minimal prime spectra of a commutative ring; among them, we mention the Zariski topology, the patch topology and the flat topology. By using these topologies, Tarizadeh and…

In this work, the set of quasi-primary ideals of a commutative ring with identity is equipped with a topology and is called quasi-primary spectrum. Some topological properties of this space are examined. Further, a sheaf of rings on the…

Semiclassical limits of generic multiparameter quantized coordinate rings A = O_q(k^n) of affine spaces are constructed and related to A, for k an algebraically closed field of characteristic zero and q a multiplicatively antisymmetric…

Brown and Goodearl stated a conjecture that provides an explicit description of the topology of the spectra of quantum algebras. The conjecture takes on a more explicit form if there exist separating Ore sets for all incident pairs of torus…

Our aim in this thesis is to use the language of deformation-quantization to understand certain quantized algebras by looking at properties of the corresponding commutative ones, and conversely to obtain results about the commutative…

Given a ring R and S one of its proper ideals, we obtain a compactification of the prime spectrum of S through a mainly algebraic process. We name it the R-nilcompactification of SpecS. We study some categorical properties of this…

We describe primitive and prime ideals in the C*-algebra C*(E) of a graph E satisfying Condition (K), together with the topologies on each of these spaces. In particular, we find that primitive ideals correspond to the set of maximal tails…

We extend the classical notion of standardly stratified $k$-algebra (stated for finite dimensional $k$-algebras) to the more general class of rings, possibly without $1,$ with enough idempotents. We show that many of the fundamental…