Alexandria Digital Research Library

A walk through quaternionic structures

Author:
Kelz, Justin
Degree Grantor:
University of California, Santa Barbara. Mathematics
Degree Supervisor:
William B. Jacob
Place of Publication:
[Santa Barbara, Calif.]
Publisher:
University of California, Santa Barbara
Creation Date:
2016
Issued Date:
2016
Topics:
Mathematics
Keywords:
Quaternionic Structure
Graph Theory
Abstract Witt Ring
Combinatorics
Witt Ring
Steiner Triple System
Genres:
Dissertations, Academic and Online resources
Dissertation:
M.A.--University of California, Santa Barbara, 2016
Description:

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.

Physical Description:
1 online resource (66 pages)
Format:
Text
Collection(s):
UCSB electronic theses and dissertations
ARK:
ark:/48907/f3zs2wnf
ISBN:
9781369340457
Catalog System Number:
990047189500203776
Rights:
Inc.icon only.dark In Copyright
Copyright Holder:
Justin Kelz
File Description
Access: Public access
Kelz_ucsb_0035N_13146.pdf pdf (Portable Document Format)