Symbolic Dynamics, Partial Dynamical Systems, Boolean Algebras and C*-algebras Generated by Partial Isometries
Abstract
Description
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 two-sided shift space is a quotient of the C*-algebra associated to the corresponding one-sided shift space.
55 pages. Version 2, which only contains minor changes compared to version 1, is identical to the preprint mentioned below
55 pages. Version 2, which only contains minor changes compared to version 1, is identical to the preprint mentioned below