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On the structure and zero divisors of the Cayley-Dickson sedenion algebra

100%

Cawagas R.

Discussiones Mathematicae - General Algebra and Applications

2004

tom 24

nr 2

251-265

The algebras ℂ (complex numbers), ℍ (quaternions), and 𝕆 (octonions) are real division algebras obtained from the real numbers ℝ by a doubling procedure called the Cayley-Dickson Process. By doubling ℝ (dim 1), we obtain ℂ (dim 2), then ℂ produces ℍ (dim 4), and ℍ yields 𝕆 (dim 8). The next doubling process applied to 𝕆 then yields an algebra 𝕊 (dim 16) called the sedenions. This study deals with the subalgebra structure of the sedenion algebra 𝕊 and its zero divisors. In particular, it shows that 𝕊 has subalgebras isomorphic to ℝ, ℂ, ℍ, 𝕆, and a newly identified algebra 𝕆̃ called the quasi-octonions that contains the zero-divisors of 𝕊.

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1 Discussiones Mathematicae - General Algebra and Applications

1 Cawagas R.

1 2004

Wyniki wyszukiwania

On the structure and zero divisors of the Cayley-Dickson sedenion algebra