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The structure of the C*-algebra of a locally injective surjection

Published online by Cambridge University Press:  10 June 2011

TOKE MEIER CARLSEN  and
KLAUS THOMSEN
TOKE MEIER CARLSEN
Affiliation:
Department of Mathematics, Norwegian University of Science and Technology, NO-7034 Trondheim, Norway (email: [email protected])
KLAUS THOMSEN
Affiliation:
Institut for matematiske fag, Ny Munkegade, DK-8000 Aarhus C, Denmark (email: [email protected])
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Abstract

In this paper we investigate the ideal structure of the C*-algebra of a locally injective surjection introduced by the second-named author. Our main result is that a simple quotient of the C*-algebra of a locally injective surjection on a compact metric space of finite covering dimension is either a full matrix algebra, a crossed product of a minimal homeomorphism of a compact metric space of finite covering dimension, or it is purely infinite and hence covered by the classification result of Kirchberg and Phillips. It follows in particular that if the C*-algebra of a locally injective surjection on a compact metric space of finite covering dimension is simple, then it is automatically purely infinite, unless the map in question is a homeomorphism. A corollary of this result is that if the C*-algebra of a one-sided subshift is simple, then it is also purely infinite.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 4 , August 2012 , pp. 1226 - 1248
Copyright
Copyright © Cambridge University Press 2011

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