# Zariski topologies on stratified spectra of quantum algebras

Source: [Zariski topologies on stratified spectra of quantum algebras](<https://www.sota2.com/research/paper/68fa50881e209131ce96c1d4>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T10:54:35.159Z

Authors: K.A. Brown, K.R. Goodearl

Published: 2013-11-01T19:38:32.000Z

## Abstract

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 different strata. A conjecture is formulated, under which the desired maps would arise from homomorphisms between certain central subalgebras of localized factor algebras of $A$. When the conjecture holds, spec $A$ and prim $A$ are then determined, as topological spaces, by a finite collection of (classical) affine algebraic varieties and morphisms between them. The conjecture is verified for ${\\cal O}\_q(GL\_2(k))$, ${\\cal O}\_q(SL\_3(k))$, and ${\\cal O}\_q(M\_2(k))$ when $q$ is a non-root of unity and the base field $k$ is algebraically closed.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1311.0271>)

[PDF](<https://arxiv.org/pdf/1311.0271.pdf>)