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C*-envelopes of tensor algebras for multivariable dynamics

Part of: Selfadjoint operator algebras Linear spaces and algebras of operators Topological dynamics

Published online by Cambridge University Press:  30 April 2010

Kenneth R. Davidson  and
Jean Roydor
Kenneth R. Davidson
Affiliation:
Pure Mathematics Department, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada ([email protected])
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Abstract

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We give a new very concrete description of the C*-envelope of the tensor algebra associated to a multivariable dynamical system. In the surjective case, this C*-envelope is described as a crossed product by an endomorphism and as a groupoid C*-algebra. In the non-surjective case, it is a full corner of such an algebra. We also show that when the space is compact the C*-envelope is simple if and only if the system is minimal.

Keywords

multivariable dynamical systemC*-envelopegroupoid C*-algebracrossed product by an endomorphismminimalsimple

MSC classification

Secondary: 47L55: Representations of (nonselfadjoint) operator algebras 47L40: Limit algebras, subalgebras of $C^*$-algebras 46L05: General theory of $C^*$-algebras 37B20: Notions of recurrence 37B99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 2 , June 2010 , pp. 333 - 351
Copyright
Copyright © Edinburgh Mathematical Society 2010