Stable rank of graph algebras. Type I graph algebras and their limits
Operator Algebras
2007-05-23 v1
Abstract
For an arbitrary countable directed graph E we show that the only possible values of the stable rank of the associated Cuntz-Krieger algebra C*(E) are 1, 2 or \infty. Explicit criteria for each of these three cases are given. We characterize graph algebras of type I, and graph algebras which are inductive limits of C*-algebras of type I. We also show that a gauge-invariant ideal of a graph algebra is itself isomorphic to a graph algebra.
Keywords
Cite
@article{arxiv.math/0211144,
title = {Stable rank of graph algebras. Type I graph algebras and their limits},
author = {Klaus Deicke and Jeong Hee Hong and Wojciech Szymanski},
journal= {arXiv preprint arXiv:math/0211144},
year = {2007}
}
Comments
13 pages, LaTeX