A new perspective on spectra of quantum spaces

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).