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

Nilpotent groups; Algebra; Mathematics

Abstract

Table algebras are generalizations of adjacency algebras, and of the character ring of a finite group. Extensions of groups by groups have been well studied, and Hirasaka and Bang have generalized this to the study of extensions of association schemes by association schemes. In this dissertation, we study central extensions of table algebras by table algebras, in the case where the extension is either class two nilpotent (which means it is an extension of a group algebra by a group algebra), or class three nilpotent (which means it is an extension of a class two nilpotent table algebra by a group algebra) with order p3 for an arbitrary prime p. We classify these algebras up to exact isomorphism. In the class two case, we determine exactly when the algebra is the adjacency algebra of an association scheme, and in the class three case, we determine which sets of the parameters of our classication determine isomorphic algebras.

Comments

Advisors: Harvey I. Blau.||Committee members: Richard Blecksmith; Michael Geline; Zhuan Ye.

Extent

78 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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