Date of Award

January 2016

Degree Type

Open Access Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Bangteng Xu

Department Affiliation

Mathematics and Statistics

Second Advisor

Patrick J. Costello

Department Affiliation

Mathematics and Statistics

Third Advisor

Mathew M. Cropper

Department Affiliation

Mathematics and Statistics

Abstract

In this paper we introduce the definition of a reality-based algebra (RBA) as well as a subclass of reality-based algebras, table algebras. Using sesquilinear forms, we prove that a reality-based algebra is semisimple. We look at a specific reality-based algebra of dimension 5 and provide formulas for the structure constants of this algebra. We determine by looking at these structure constants and setting conditions on specific structural components when this particular reality-based algebra is a table algebra. In fact, this will be a noncommutative table algebra of dimension 5.

Included in

Algebra Commons

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