Bounds on the levels of composition algebras

Files in This Item:
File Description SizeFormat 
MPRIA_OShea_2010.pdf158.03 kBAdobe PDFDownload
Title: Bounds on the levels of composition algebras
Authors: O'Shea, James
Permanent link:
Date: 2010
Online since: 2010-10-13T16:08:08Z
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.
Funding Details: Irish Research Council for Science, Engineering and Technology
Other funder
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: Quadratic formFunction fieldLevelSublevelQuaternion algebraOctonion algebra
Subject LCSH: Forms, Quadratic
Cayley numbers (Algebra)
DOI: 10.3318/PRIA.2010.110.1.21
Other versions:
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

Show full item record

Google ScholarTM



This item is available under the Attribution-NonCommercial-NoDerivs 3.0 Ireland. No item may be reproduced for commercial purposes. For other possible restrictions on use please refer to the publisher's URL where this is made available, or to notes contained in the item itself. Other terms may apply.