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...atrices with entries in the Cayley-Graves algebra O_C of complex octonions ... The space <math>H_3 (O_C)</math> of such matrices which are [[Hermitian Complex octonions have been used to describe the generations of [[quark]]s and [[lepton]]s.<r ...

...ve at least one solution, independent of the order of the parenthesis (the octonions are a [[non-associative algebra]]).<ref>{{Cite journal|last1=Liu|first1=Min ...

==Octonions== The octonions are a [[normed division algebra]] over the real numbers, the largest such a ...

...=<!--none-->}}. ([http://nugae.wordpress.com/2007/04/25/on-quaternions-and-octonions/ Review]). ...

...ohibits the existence of algebraic structures like the [[quaternion]]s and octonions in dimensions other than 2, 4, and 8. The first [[exotic sphere]]s ever dis ...

...ly for his theory of [[braided Hopf algebra]]s and for a new view of the [[octonions]]. Although many regard Majid as a pure mathematician, his motivation and e ...additive braided groups. Other well-known work includes a picture of the [[octonions]] as associative in a certain symmetric monoidal category. ...

...s and are thus not a [[division algebra]]. Furthermore, in contrast to the octonions, both algebras do not even have the property of being [[Alternative_algebra ...taduonion multiplication table, which are listed below. In comparison, the octonions have 7 such triples, the sedenions have 35, while the sexagintaquatronions ...

...lgebras are the real numbers, the complex numbers, the quaternions and the octonions. ...ternions) and {{math|1=''n'' ≥ 3}} or if {{mvar|A}} is nonassociative (the octonions) and {{math|1=''n'' = 3}}. ...

* isomorphic to the [[octonions]] if non-associative but [[alternative algebra|alternative]]. ...

...ssue = 2 | page = 186 | year = 2002 | url = https://math.ucr.edu/home/baez/octonions/node14.html | doi = 10.1090/S0273-0979-01-00934-X | arxiv = math/0105155| m ...

...1+728 || The Chevalley group of type G₂ acting on the imaginary octonions of the octonion algebra over GF(3); two classes ...

...anes (over the real numbers, the complex numbers, the quaternions, and the octonions) are compact [[manifold]]s of dimension <math>2^m,\, 1 \le m \le 4</math>. ...

...Octonion#Integral_octonions|integral octonions]] of norm 1. Because the [[octonions]] are a nonassociative [[normed division algebra]], these 240 points have a ...