On closed subsets of non-commutative association schemes of rank 6

Authors

Jose Vera, University of Texas at Brownsville

Date of Award

11-2013

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Paul-Hermann Zieschang

Second Advisor

Dr. Vesselin Vatchev

Third Advisor

Dr. James R. Maissen

Abstract

The notion of an association scheme is a generalization of the concept of a group. In fact, the so-called thin association schemes correspond in a well-understood way to groups. In this thesis, we look at the structure of non-commutative association schemes of rank 6. We will show that a non-normal closed subset of a noncommutative association scheme of rank 6, must have rank 2. The so-called Coxeter schemes of rank 6 which we present in Section 4 provide examples of association schemes of rank 6 with non-normal closed subsets of rank 2. It is shown that normal closed subsets of imprimitive non-commutative schemes of rank 6 must have rank 2 or 3, so we will also look at the structure of association schemes of rank 6, with symmetric normal closed subsets of rank 3, and the structure of association schemes of rank 6 when they have non-symmetric closed subsets of rank 3. We will additionally see how to construct an association scheme of rank 6 with non-symmetric normal closed subsets.

Comments

Copyright 2013 Jose Vera. All Rights Reserved.

Granting Institution

University of Texas Brownsville