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A walk through quaternionic structures

<p> 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 = &ndash;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.</p>

Identiferoai:union.ndltd.org:PROQUEST/oai:pqdtoai.proquest.com:10192389
Date18 November 2016
CreatorsKelz, Justin
PublisherUniversity of California, Santa Barbara
Source SetsProQuest.com
LanguageEnglish
Detected LanguageEnglish
Typethesis

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