Bounds on the levels of composition algebras

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Title: Bounds on the levels of composition algebras
Authors: O'Shea, James
Permanent link: http://hdl.handle.net/10197/2518
Date: 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.
Funding Details: Irish Research Council for Science, Engineering and Technology
Other funder
Type of material: Journal Article
Publisher: Royal Irish Academy
Copyright (published version): Royal Irish Academy
Keywords: Quadratic form;Function field;Level;Sublevel;Quaternion algebra;Octonion algebra
Subject LCSH: Forms, Quadratic
Quaternions
Cayley numbers (Algebra)
DOI: 10.3318/PRIA.2010.110.1.21
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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