Publication Date

2014

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

Abstract

The structure of a standard integral table algebra can sometimes be determined by the multiplicities of the irreducible characters for that table algebra. In particular, it has been shown that a standard table algebra whose multiplicities are all equal (except for the trivial one) must be commutative. This dissertation seeks to extend the technique of using multiplicities to determine the structure of standard table algebras. For a commutative standard table algebra, we show that there exists exactly one character with nontrivial multiplicity if and only if the table basis is the wreath product of a two-dimensional subalgebra and an abelian group. Additionally, we show that a noncommutative standard integral table algebra with exactly one character (of degree two) that has nontrivial multiplicity must have one of two structures, both corresponding to a partial wreath product (B, D, C), where D has dimension 6 or 8, where C has dimension 2 or 3, and where the structure constants are explicitly determined by certain parameters that are bounded by a function of the nontrivial multiplicity.

Comments

Advisors: Harvey Blau.||Committee members: Michael Geline; Deepak Naidu.

Extent

85 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

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