Stable rank of graph algebras. Type I graph algebras and their limits

By K. Deicke, J. Hong, W. Szymański. 2002

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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 ∞. 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.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

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