C*-envelopes of tensor algebras for multivariable dynamics

Details C*-envelopes of tensor algebras for multivariable dynamics C*-envelopes of tensor algebras for multivariable dynamics

2008-11-29

arxiv.org/abs/0812.0096v1

Mathematics

Operator Algebras

21 pages, submitted to Proceedings of the Edinburgh Mathematical Society

Scientific paper

We give a new very concrete description of the C*-envelope of the tensor algebra associated to 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 a such an algebra. We also show that when the space is compact, then the C*-envelope is simple if and only if the system is minimal.

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