On the K-Theory of Generalized Bunce-Deddens Algebras

Graduate Thesis Or Dissertation

Citations

Citeable URL: https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/3j333228j

Abstract

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.

Creator