A latticed total K-theory

TL;DR

This paper introduces latticed total K-theory, a new invariant for classifying a broad class of separable C*-algebras of real rank zero, including those with finite and infinite projections.

Contribution

It develops a novel invariant, latticed total K-theory, and proves a classification theorem for many C*-algebras of real rank zero using this invariant.

Findings

Classification of many C*-algebras with finite and infinite projections

Introduction of latticed total K-theory as a new invariant

A classification theorem for a large class of real rank zero C*-algebras

Abstract

In this paper, a new invariant was built towards the classification of separable C*-algebras of real rank zero, which we call latticed total K-theory. A classification theorem is given in terms of such an invariant for a large class of separable C*-algebras of real rank zero arising from the extensions of finite and infinite C*-algebras. Many algebras with both finite and infinite projections can be classified.