Bounds on the levels of composition algebras
|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
|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
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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