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Embedding covariance algebras of flows into $AF$-algebras

Published online by Cambridge University Press:  01 June 1999

MICHAEL V. PIMSNER
MICHAEL V. PIMSNER
Affiliation:
University of Pennsylvania, School of Arts and Sciences, Department of Mathematics, 209 South 33rd Street, Philadelphia, PA 19104-6395, USA
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Abstract

Suppose that $\{\alpha_t\}_{t\in \mathbb{R}}$ is a flow on the compact metrizable space $X$. We prove that a necessary and sufficient condition for the existence of an embedding (injective $*$-homomorphism) of the crossed product $C(X)\rtimes_\alpha \mathbb{R}$ into some $AF$-algebra is that every point of $X$ be chain recurrent in the sense of Conley.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 3 , June 1999 , pp. 723 - 740
Copyright
1999 Cambridge University Press

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