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Showing 1 to 4 of 4 for “"Octonion"”.
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Topics in Moufang Loops
… of proving this result we define the generalized octonion loops, a variety of Moufang loops which behave analogously to the generalized quaternion groups. We proceed to investigate para-F quasigroups, a variety of quasigroups which we show are antilinear over Moufang loops. We briefly depart from …
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Cayley-Dickson Loops
… are real numbers, complex numbers, quaternions, octonions, sedenions). Starting at the octonions, Cayley-Dickson algebras and loops become nonassociative, which presents a significant challenge in their study.</p> <p>We begin by describing basic properties of the Cayley–Dickson loops …
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Graded-commutative nonassociative algebras: higher octonions and Krichever-Novikov superalgebras; their structures, combinatorics and non-trivial cocycles.
… (resp. $\bbO_{n}$) generalizing the algebra of octonion numbers $\bbO$. This generalization is similar to the one of the algebra of quaternion numbers in Clifford algebras. Introduced by Morier-Genoud and Ovsienko, these algebras have a natural $\bbZ_2^n$-grading ($p+q =n$), and they are …
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Octonions and the Exceptional Lie Algebra g_2
We first introduce the octonions as an eight dimensional vector space over a field of characteristic zero with a multiplication defined using a table. We also show that the multiplication rules for octonions can be derived from a special graph with seven vertices call the Fano Plane. Next we …