More precisely an integral octonion of norm " mn " can be written as a product of integral octonions of norms " m " and " n ".
22.
The most well-known example of an octonion algebra is the classical octonions, which are an octonion algebra over "'R "', the field of real numbers.
23.
The most well-known example of an octonion algebra is the classical octonions, which are an octonion algebra over "'R "', the field of real numbers.
24.
Since any two octonion " F "-algebras become isomorphic over the algebraic closure of " F ", one can apply the ideas of non-abelian Galois cohomology.
25.
The other is that the concept is an analogue to the octonion algebras, and quadratic Jordan division algebras of degree 3, that give rise to Moufang 3-gons and 6-gons.
26.
But " S " 7 is not a group in this way because octonion multiplication is not associative, nor can it be given any other continuous multiplication for which it is a group.
27.
His research interests are Yang-Mills gauge theories, supersymmetry, supergravity, quaternion and octonion algebras, spin structures, generalised theories of gravity, cosmological solutions, integrable systems and phase space quantisation.
28.
It is a theorem of Adolf Hurwitz that the " F "-isomorphism classes of the norm form are in one-to-one correspondence with the isomorphism classes of octonion " F "-algebras.
29.
The octonion algebra for " N " is a division algebra if and only if the form " N " is algebraically closed or a finite field, these are the only octonion algebras over " F ".
30.
The octonion algebra for " N " is a division algebra if and only if the form " N " is algebraically closed or a finite field, these are the only octonion algebras over " F ".
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