A classification theorem for direct limits of extensions of circle algebras by purely infinite C*-algebras

TL;DR

This paper establishes a classification theorem for a specific class of C*-algebras formed as direct limits of extensions of circle algebras by purely infinite C*-algebras, using a comprehensive invariant.

Contribution

It introduces a new classification framework for these C*-algebras based on a detailed invariant involving projections, partial isometries, a map d, and total K-theory.

Findings

Classification achieved for the specified C*-algebras class

Invariant effectively distinguishes non-isomorphic algebras

Framework extends existing classification results

Abstract

We give a classification theorem for a class of C*-algebras which are direct limits of extensions of circle algebras by purely infinite C*-algebras. The invariant consists of the following: (1) the set of Murray-von Neumann equivalence classes of projections; (2) the set of homotopy classes of hyponormal partial isometries; (3) a map d; and (4) total K-theory.