Publication Date

2016

Document Type

Dissertation/Thesis

First Advisor

Blau, Harvey I., 1942-

Degree Name

Ph.D. (Doctor of Philosophy)

Legacy Department

Department of Mathematical Sciences

LCSH

Algebra; Coxeter groups

Abstract

Table algebras are algebraic structures which generalize distinct but related configurations such as the adjacency algebra of an association scheme, a group algebra (and its center), and the algebra formed by the characters of that group. In this dissertation, we study table algebras generated by involutions, which are associated with Coxeter (association) schemes, an alternate representation of regular Tits buildings. Coxeter table algebras, like Coxeter schemes, are defined by two characteristics, constrainedness and the exchange condition. The exchange condition for table algebras and schemes generalizes the exchange condition for Coxeter groups. Our first principal result shows that, for certain cases, the exchange condition for Coxeter schemes and table algebras can be replaced by a weaker condition on the generating set. We then study Coxeter table algebras, which generalize adjacency algebras of finite Coxeter schemes. A direct correspondence between Coxeter table algebras and generic Hecke algebras (as defined by Bourbaki and Couillens) results in a full classification of Coxeter table algebras. Lastly, we examine which Coxeter table algebras arise from Coxeter schemes, which we can also classify fully except in some small cases.

Comments

Advisors: Harvey I. Blau.||Committee members: Douglas Bowman; Michael Geline; Jeffrey Thunder.||Includes bibliographical references.||Includes illustrations.

Extent

74 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.

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