Stable rank of Leavitt path algebras of arbitrary graphs

TL;DR

This paper extends the calculation of the stable rank of Leavitt path algebras from row-finite graphs to arbitrary graphs, using desingularization techniques and characterizing purely infinite simple quotients.

Contribution

It generalizes the stable rank computation to all directed graphs and applies desingularizing methods to handle infinite cases.

Findings

Stable rank computed for arbitrary graphs.

Characterization of purely infinite simple quotients.

Extension of previous row-finite results.

Abstract

The stable rank of Leavitt path algebras of row-finite graphs was computed by Ara and Pardo. In this paper we extend this for an arbitrary directed graph. In some parts, we proceed our computation as the row-finite case while in some parts we use the knowledge about row-finite setting by applying the desingularizing method due to Drinen and Tomforde. In particular, we characterize purely infinite simple quotients of a Leavitt path algebra.