Bounds on the levels of composition algebras

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Author(s)
Uri
Date Issued
2010
Date Available
13T16:08:08Z October 2010
Abstract
Certain families of quaternion and octonion algebras are conjectured to be of level and sublevel n. A proof of this conjecture is offered in the case where n is a power of two. Hoffmann's proof of the existence of infinitely many new values for the level of a quaternion algebra is generalised and adapted. Alternative constructions of quaternion and octonion algebras are introduced and justified in the case where n is a multiple of a two power.
Sponsorship
Irish Research Council for Science, Engineering and Technology
Other funder
Other Sponsorship
European RTN network "Algebraic K-Theory, Linear Algebraic Groups and Related Structures"
Type of Material
Journal Article
Publisher
Royal Irish Academy
Journal
Mathematical Proceedings of the Royal Irish Academy
Volume
110
Start Page
21
End Page
30
Copyright (Published Version)
Royal Irish Academy
Keywords
Subject – LCSH
Forms, Quadratic
Quaternions
Cayley numbers (Algebra)
DOI
Web versions
Language
English
Status of Item
Peer reviewed
ISSN
1393-7197 (Print)
2009-0021 (Online)
This item is made available under a Creative Commons License
Owning collection
Mathematics and Statistics Research Collection