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||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
|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 form; Function field; Level; Sublevel; Quaternion algebra; Octonion algebra||Subject LCSH:||Forms, Quadratic
Cayley numbers (Algebra)
|DOI:||10.3318/PRIA.2010.110.1.21||Other versions:||http://dx.doi.org/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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