Stability of -algebras associated to graphs
Author:
Mark Tomforde
Translated by:
Journal:
Proc. Amer. Math. Soc. 132 (2004), 1787-1795
MSC (2000):
Primary 46L55
DOI:
https://doi.org/10.1090/S0002-9939-04-07411-8
Published electronically:
January 30, 2004
MathSciNet review:
2051143
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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 03755-3551
Address at time of publication:
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Email:
tomforde@math.uiowa.edu
DOI:
https://doi.org/10.1090/S0002-9939-04-07411-8
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