Stability of algebras associated to graphs
Author:
Mark Tomforde
Translated by:
Journal:
Proc. Amer. Math. Soc. 132 (2004), 17871795
MSC (2000):
Primary 46L55
Published electronically:
January 30, 2004
MathSciNet review:
2051143
Fulltext PDF Free Access
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Abstract: We characterize stability of graph algebras by giving five conditions equivalent to their stability. We also show that if is a graph with no sources, then is stable if and only if each vertex in can be reached by an infinite number of vertices. We use this characterization to realize the stabilization of a graph algebra. Specifically, if is a graph and is the graph formed by adding a head to each vertex of , then is the stabilization of ; that is, .
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Additional Information
Mark Tomforde
Affiliation:
Department of Mathematics, Dartmouth College, Hanover, New Hampshire 037553551
Address at time of publication:
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Email:
tomforde@math.uiowa.edu
DOI:
http://dx.doi.org/10.1090/S0002993904074118
PII:
S 00029939(04)074118
Received by editor(s):
June 14, 2002
Received by editor(s) in revised form:
March 1, 2003
Published electronically:
January 30, 2004
Communicated by:
David R. Larson
Article copyright:
© Copyright 2004
American Mathematical Society
