C*-envelopes of tensor algebras for multivariable dynamics
  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. 
K.R. Davidson and J. Roydor