- Algebras Generated by Partial Isometries

We associate to each discrete partial dynamical system a universal C-algebra generated by partial isometries satisfying relations given by a Boolean algebra connected to the discrete partial dynamical system in question. We show that for symbolic dynamical systems like one-sided and two-sided shift spaces and topological Markov chains with an arbitrary state space the C-algebras usually associated to them, can be obtained in this way. As a consequence of this, we will be able to show that for two-sided shift spaces having a certain property, the crossed product of the twosided shift space is a quotient of the C-algebra associated to the corresponding one-sided shift space.