Journal of Operator Theory

Volume 61, Issue 2, Spring 2009 pp. 439-457.

Classification of certain inductive limit type actions of ${\Bbb R}$ on $C^*$-algebras

Authors: Andrew J. Dean
Author institution: Department of Mathematical Sciences, Lakehead University, 955 Oliver Road, Thunder Bay, Ontario, Canada, P7B 5E1

Summary: In this paper we present a classification, up to equivariant isomorphism, of $C^*$-dynamical systems $(A,{\Bbb R},\a )$ arising as inductive limits of directed systems $\{ (A_n,{\Bbb R},\a_n),\varphi_{nm}\}$ where each $A_n$ is a finite direct sum of matrix algebras over graphs, the $\varphi_{nm}$ are unital and injective, and the $\a_n$s are generated by inner $*$-derivations coming from diagonalisable self-adjoint elements with distinct eigenvalues.

Keywords: Classification, $C^*$-dynamical systems, derivations

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