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Symbolic Dynamics, Partial Dynamical Systems, Boolean Algebras and C*-algebras Generated by Partial Isometries

Toke Meier Carlsen
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Abstract

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.

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Toke Meier Carlsen. 2006-10-12. Symbolic Dynamics, Partial Dynamical Systems, Boolean Algebras and C*-algebras Generated by Partial Isometries. https://arxiv.org/abs/math/0604165

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