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.
| Identifer | oai:union.ndltd.org:MSSTATE/oai:scholarsjunction.msstate.edu:td-7127 |
| Date | 10 May 2024 |
| Creators | Hebert, Shelley David |
| Publisher | Scholars Junction |
| Source Sets | Mississippi State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Theses and Dissertations |
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