Semicrossed Products of Operator Algebras: A Survey
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.