Date of Award
January 2016
Degree Type
Open Access Thesis
Document Type
Master 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.
Copyright
Copyright 2016 Rachel Victoria Barber
Recommended Citation
Barber, Rachel Victoria, "Low-Dimensional Reality-Based Algebras" (2016). Online Theses and Dissertations. 336.
https://encompass.eku.edu/etd/336
