C*-algebras of labeled graphs and *-commuting endomorphisms

Abstract

My research lies in the general area of functional analysis. I am particularly interested in C∗-algebras and related dynamical systems. From the very beginning of the theory of operator algebras, in the works of Murray and von Neumann dating from the mid 1930′s, dynamical systems and operator algebras have led a symbiotic existance. Murray and von Neumann’s work grew from a few esoteric, but clearly original and prescient papers, to a major river of contemporary mathematics. My work lies at the confluence of two important tributaries to this river. On the one hand, the operator algebras that I study are C∗-algebras that are built from graphs. On the other, the dynamical systems on which I focus are symbolic dynamical systems of various types. My goal is to use dynamical systems theory to construct new and interesting C∗-algebras and to use the algebraic invariants of these algebras to reveal properties of the dynamics. My work has two fairly distinct strands: One deals with C∗-algebras built from irreversible dynamical systems. The other deals with group actions on graph C∗-algebras and their generalizations. Abstract Approved: Thesis SupervisorApproved: Thesis Supervisor Title and Department