Operator algebras for multivariable dynamics

Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $ to X$ for $1 le i le n$. To this the authors associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra $mathcalA(X,tau)$ and the semicrossed product $mathrmC0(X)timestaumathbbFn+$. They develop the necessary dilation theory for both models. In particular, they exhibit an explicit family of boundary representations which determine the C*-envelope of the tensor algebra.Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $ to X$ for $1 le i le n$. To this the authors associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra $mathcalA(X,tau)$ and the semicrossed product $mathrmC0(X)timestaumathbbFn+$. They develop the necessary dilation theory for both models. In particular, they exhibit an explicit family of boundary representations which determine the C*-envelope of the tensor algebra.