Publication Date

2015

Document Type

Dissertation/Thesis

First Advisor

Blau, Harvey I., 1942-

Degree Name

Ph.D. (Doctor of Philosophy)

Legacy Department

Department of Mathematical Sciences

LCSH

Mathematics; Commutative algebra--Research; Group rings--Research

Abstract

Fusion rings are a class of table algebras that generalize group rings with basis the group and character rings of a finite group with basis the irreducible characters. Examples are the Grothendieck rings of fusion categories, algebraic structures that are related to conformal field theory. When considering the character ring of a group as a fusion ring, the usual degree of a character coincides with the value assigned by the degree map. Hence classifying fusion rings based on the degree set is a generalization of classifying groups based on the degrees of the irreducible characters. The main theorem classifies real fusion rings with degrees 1 and 4 such that all stabilizers have the same order (so-called stabilizer-regular fusion rings).

Comments

Advisors: Harvey Blau.||Committee members: John Beachy; Douglas Bowman; Ilya Krishtal.

Extent

92 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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