Date of Award

Spring 1-1-2018

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Judith Packer

Second Advisor

Carla Farsi

Third Advisor

Martin Walter

Fourth Advisor

Robin Deeley

Fifth Advisor

Elizabeth Gillaspy

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*(T1T2)⋊σ2 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.

Included in

Algebra Commons

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