A groupoid appproach to Cuntz-Krieger algebras

Specialeforsvar ved Kevin Aguyar Brix

Titel: A groupoid approach to Cuntz-Krieger algebras

Abstract: An irreducible square matrix with entries either 0 or 1 gives rise to a plethora of interesting mathematical objects.
One can construct the one-sided topological Markov shift on which the shift acts. Alternatively, one can construct a $C^*$-algebra, the Cuntz-Krieger algebra, or a groupoid.
In 2010, K. Matsumoto introduced the notion of continuous orbit equivalence between topological Markov shifts and showed that this can be characterized in terms of C*-isomorphisms between the Cuntz-Kriegers algebras which preserve a certain abelian C*-subalgebra.
In a recent paper, published in 2014, K. Matsumoto and H. Matui provided the final piece of a characterization of continuous orbit equivalence between Markov shifts. This includes the notions of C*-algebras, groups and groupoids. In this thesis, we give a proof of this classification result.
Along the way, we will see how to realize the Cuntz-Krieger algebra as a groupoid C*-algebra.

Vejleder:    Søren Eilers
Censor:      Toke Meier Carlsen, Færøernes Universitet