Semiprojectivity for certain purely infinite C*-algebras

TL;DR

This paper proves that a class of simple, separable, nuclear purely infinite C*-algebras with specific K-theory properties are semiprojective, by representing them as C*-algebras of infinite directed graphs.

Contribution

It establishes semiprojectivity for certain purely infinite C*-algebras using graph C*-algebra representations, expanding understanding of their structural properties.

Findings

Classifiable simple separable nuclear purely infinite C*-algebras with finitely generated, torsion-free K_1 are semiprojective.

These algebras can be realized as C*-algebras of infinite directed graphs.

Provides a new approach to studying semiprojectivity via graph C*-algebras.

Abstract

It is proved that classifiable simple separable nuclear purely infinite C*-algebras having finitely generated K-theory and torsion-free K_1 are semiprojective. This is accomplished by exhibiting these algebras as C*-algebras of infinite directed graphs.