Stably finite extensions of rank-two graph C*-algebras

TL;DR

This paper investigates conditions under which extensions of rank-two graph C*-algebras are stably finite, using K-theory calculations and a theorem by Spielberg, with illustrative examples.

Contribution

It provides a new sufficient condition for stable finiteness of 2-graph C*-algebras based on K-theory and hereditary subgraph analysis.

Findings

Derived a K-theory map for hereditary subgraph inclusion

Established a sufficient condition for stable finiteness

Provided illustrative examples demonstrating the results

Abstract

We study stable finiteness of extensions of 2-graph C*-algebras determined by saturated hereditary sets of vertices. We use two iterations of the Pimsner-Voiculescu sequence to calculate the map in K-theory induced by the inclusion of a hereditary subgraph into the larger 2-graph it lives in. We then apply a theorem of Spielberg about stable finiteness of extensions to provide a sufficient condition for the C*-algebra of the larger 2-graph to be stably finite. We illustrate our results with examples.