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STABLE RANK OF LEAVITT PATH ALGEBRAS OF ARBITRARY GRAPHS

Part of: Modules, bimodules and ideals

Published online by Cambridge University Press:  12 December 2012

HOSSEIN LARKI  and
ABDOLHAMID RIAZI
HOSSEIN LARKI*
Affiliation:
Department of Mathematics, Faculty of Mathematics and Computer Science, Shahid Chamran University, Ahwaz, Iran
ABDOLHAMID RIAZI
Affiliation:
Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology,424 Hafez Ave., 15914 Tehran, Iran email riazi@aut.ac.ir
*
✉h.larki@aut.ac.irh.larki@gmail.com
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Abstract

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The stable rank of Leavitt path algebras of row-finite graphs was computed by Ara and Pardo. In this paper we extend this to an arbitrary directed graph. In part our computation proceeds as for the row-finite case, but we also use knowledge of the row-finite setting by applying the desingularising method due to Drinen and Tomforde. In particular, we characterise purely infinite simple quotients of a Leavitt path algebra.

Keywords

Leavitt path algebrastable rankpurely infinite quotient

MSC classification

Secondary: 16D70: Structure and classification (except as in ), direct sum decomposition, cancellation

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 2 , October 2013 , pp. 206 - 217
Copyright
Copyright ©2012 Australian Mathematical Publishing Association Inc. 

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