Mathematical Physics

    

Octonions, Broctonions and Sedenions

Authors: Richard D. Lockyer

There are 128 different eight-dimensional algebras that have seven Quaternion subalgebras with common construction. Sixteen of these are proper Octonion Algebras. The remaining 112 forms are one Quaternion subalgebra orientation off of a proper Octonion Algebra orientation, one may say a broken Octonion Algebra. An appropriate name for them would be “Broctonion Algebras”. It is impossible to orient a Sedenion Algebra without Broctonion subalgebras, and they are the source of all Sedenion Algebra primitive zero divisors. It is possible though, to form Sedenion Algebras without a single proper Octonion subalgebra. This paper defines all Broctonion forms and explores their relationship to Sedenion Algebras.

Comments: 12 Pages. Keywords: Octonions, Octonion Algebra, Sedenions, Sedenion Algebra, zero divisors, Broctonion Algebra

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Submission history

[v1] 2022-03-18 13:49:55

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