2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209219We 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.21 pages, submitted to Proceedings of the Edinburgh Mathematical SocietyOperator Algebras47L55, 47L40, 46L05, 37B20, 37B99text