ON THE STABILITY OF A FIXED POINT ALGEBRA C^{*}(E)^{γ} OF A GAUGE ACTION ON A GRAPH C^{*}-ALGEBRA

- Journal title : Journal of the Korean Mathematical Society
- Volume 46, Issue 3, 2009, pp.657-673
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2009.46.3.657

Title & Authors

ON THE STABILITY OF A FIXED POINT ALGEBRA C^{*}(E)^{γ} OF A GAUGE ACTION ON A GRAPH C^{*}-ALGEBRA

Jeong, Ja-A.;

Jeong, Ja-A.;

Abstract

The fixed point algebra of a gauge action on a graph -algebra and its AF subalgebras associated to each vertex v do play an important role for the study of dynamical properties of . In this paper, we consider the stability of (an AF algebra is either stable or equipped with a (nonzero bounded) trace). It is known that is stably isomorphic to a graph -algebra which we observe being stable. We first give an explicit isomorphism from to a full hereditary -subalgebra of and then show that is stable whenever is so. Thus cannot be stable if admits a trace. It is shown that this is the case if the vertex matrix of E has an eigenvector with an eigenvalue > 1. The AF algebras are shown to be nonstable whenever E is irreducible. Several examples are discussed.

Keywords

graph -algebra;stable -algebra;fixed point algebra;full hereditary -subalgebra;

Language

English

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