Dissertation/Thesis Abstract

A walk through quaternionic structures
by Kelz, Justin, M.A., University of California, Santa Barbara, 2016, 66; 10192389
Abstract (Summary)

In 1980, Murray Marshall proved that the category of Quaternionic Structures is naturally equivalent to the category of abstract Witt rings. This paper develops a combinatorial theory for finite Quaternionic Structures in the case where 1 = –1, by demonstrating an equivalence between finite quaternionic structures and Steiner Triple Systems (STSs) with suitable block colorings. Associated to these STSs are Block Intersection Graphs (BIGs) with induced vertex colorings. This equivalence allows for a classification of BIGs corresponding to the basic indecomposable Witt rings via their associated quaternionic structures. Further, this paper classifies the BIGs associated to the Witt rings of so-called elementary type, by providing necessary and sufficient conditions for a BIG associated to a product or group extension.

Indexing (document details)
Advisor: Jacob, William B.
Commitee: Bigelow, Stephen, McCammond, Jon
School: University of California, Santa Barbara
Department: Mathematics
School Location: United States -- California
Source: MAI 56/01M(E), Masters Abstracts International
Subjects: Mathematics
Keywords: Abstract Witt ring, Combinatorics, Graph theory, Quaternionic structure, Steiner triple system, Witt ring
Publication Number: 10192389
ISBN: 9781369340457
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