$C^∗$-envelopes of tensor algebras for multivariable dynamics

Kenneth R. Davidson (1) , Jean Roydor (2)

1 Department of Pure Mathematics [Waterloo]
2 IMB - Institut de Mathématiques de Bordeaux

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.

Domaines: Analyse fonctionnelle [math.FA]

Kenneth R. Davidson, Jean Roydor. $C^∗$-envelopes of tensor algebras for multivariable dynamics. Proc. Edinb. Math. Soc., 2010, pp.Proc. Edinb. Math. Soc. (2) 53 (2010), no. 2, 333-351. ⟨hal-01016322⟩