A decomposition theorem for real rank zero inductive limits of 1-dimensional non-commutative CW complexes

TL;DR

This paper proves a decomposition theorem for connecting homomorphisms in real rank zero C*-algebras formed as inductive limits of 1-dimensional non-commutative CW complexes, aiding their classification.

Contribution

It introduces a decomposition result for connecting homomorphisms in real rank zero inductive limits of non-commutative CW complexes, advancing classification methods.

Findings

Decomposition theorem for connecting homomorphisms

Application to classification of real rank zero C*-algebras

Enhanced understanding of inductive limit structures

Abstract

In this paper, we consider the real rank zero $\mathrm{C}^*$-algebras which can be written as an inductive limit of the Elliott-Thomsen building blocks and prove a decomposition result for the connecting homomorphisms; this technique will be used in the classification theorem.