Date of Award

Spring 1-1-2012

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

First Advisor

David Grant

Second Advisor

Sebastian Casalaina-Martin

Third Advisor

Mahesh Varanasi

Abstract

Space-time codes are used to reliably send data from multiple transmit antennas and are directly related to non-associative division algebras. While interested in classifying and building space-time codes, using this relationship this thesis considers the corresponding problem of classifying and building non-associative division algebras. The first four chapters develop the problem and give a classification of 4-dimensional non-associative division algebras. Using the classification in chapter 4, I identify a class with no previously known examples. The rest of the thesis develops the background material necessary to understand two methods to build new non-associative division algebras in the aforementioned class. The thesis ends with the methods to build new non-associative division algebras and two examples using the methods. The intermediary steps used in the construction of the examples use tools from the arithmetic of elliptic curves over number fields, commutative algebra, and algebraic number theory.

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