Theses and Dissertations

ORCID

https://orcid.org/0009-0002-4081-3586

Advisor

McBride, Matthew

Committee Member

Smith , Robert

Committee Member

Dang, Hai

Committee Member

Fabel, Paul

Committee Member

Diegel, Amanda

Date of Degree

5-10-2024

Original embargo terms

Immediate Worldwide Access

Document Type

Dissertation - Open Access

Major

Mathematical Sciences

Degree Name

Doctor of Philosophy (Ph.D)

College

College of Arts and Sciences

Department

Department of Mathematics and Statistics

Abstract

I define and analyze the Hensel-Steinitz algebra ����(��), a crossed product C∗-algebra associated with multiplication maps on continuous functions on the ring of ��-adic integers. In ����(��), I define an ideal and identify it with a known algebra. From this, I construct a short exact sequence conveying the structure of the algebras. I further identify smooth subalgebras within both ����(��) and its ideal, classify derivations on those algebras, and compare the classification with derivations on other smooth algebras. I also analyze the algebras associated with multiplication maps based on the multiplier being a root of unity, not a root of unity, or not invertible in the ��-adic integers. In the case of the multiplier being a root of unity and the quotient group therefore being finite, unexpected additional structure is found.

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