Date of Award
Doctor of Philosophy (PhD)
We consider a ℤ-action σ on a directed graph -- in particular a rooted tree T -- inherited from the odometer action. This induces a ℤ-action by automorphisms on C*(T). We show that the resulting crossed product C*(T) ⋊σℤ is strongly Morita equivalent to the Bunce-Deddens algebra. The Pimsner-Voiculescu sequence allows us to reconstruct the K-theory for the Bunce-Deddens algebra in a new way using graph methods. We then extend to a ℤk-action σ̃ on a k-graph when k = 2, show that C*(T1 ✕ T2)⋊σℤ2 is strongly Morita equivalent to a generalized Bunce-Deddens algebra of type Orfanos, and invoke the Künneth theorem to determine this new crossed product's K-theory. We end by generalizing the results for all k.
Davidoff, Nathan, "On the K-Theory of Generalized Bunce-Deddens Algebras" (2018). Mathematics Graduate Theses & Dissertations. 68.