A new perspective on spectra of quantum spaces

TL;DR

This paper introduces a novel operator algebra framework to explicitly parametrize the spectra of C*-algebras associated with quantum spaces like spheres and projective spaces.

Contribution

It provides a new perspective by constructing a non-self-adjoint operator algebra and a functor linking its representations to those of the quantum space C*-algebras.

Findings

Constructed a family of one-dimensional representations parametrizing the spectrum.

Established an explicit functor connecting representations of the operator algebra to the quantum space C*-algebras.

Provided a new method to analyze spectra of quantum space C*-algebras.

Abstract

We consider a class of C*-algebras C(X) associated with quantum spaces such as spheres, projective spaces, and lens spaces. We introduce a non-self-adjoint operator algebra A together with an explicit functor from the category of representations of A to that of C(X). We then construct explicitly a family of one-dimensional representations of A that parametrise the entire spectrum of C(X).