Semiprojectivity and properly infinite projections in graph C*-algebras

TL;DR

This paper characterizes when unital graph C*-algebras are semiprojective, disproves two conjectures by Blackadar, and analyzes properly infinite projections within these algebras.

Contribution

It provides a complete characterization of semiprojectivity in unital graph C*-algebras and refutes existing conjectures through detailed projection analysis.

Findings

Identifies conditions for semiprojectivity in unital graph C*-algebras

Disproves two conjectures by Blackadar

Analyzes properly infinite projections in these algebras

Abstract

We give a complete description of which unital graph C*-algebras are semiprojective, and use it to disprove two conjectures by Blackadar. To do so, we perform a detailed analysis of which projections are properly infinite in such C*-algebras.