Spectra of quantum algebras

TL;DR

This survey reviews the current understanding and conjectures regarding the prime and primitive spectra of quantum algebras, especially quantized coordinate rings, exploring their topological structures and connections to classical algebraic varieties.

Contribution

It compiles and discusses known results and conjectures about the spectra of quantum algebras, highlighting their topological and geometric relationships.

Findings

Summarizes known spectral properties of quantum algebras

Discusses conjectures about the structure of spectra

Explores links between quantum spectra and classical varieties

Abstract

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 algebraic varieties, and their relations to each other are discussed.