Sedenion

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In abstract algebra, the sedenions form a 16-dimensional noncommutative and nonassociative algebra over the real numbers, usually represented by the capital letter S, boldface S or blackboard bold ⁠ S {\displaystyle \mathbb {S} } ⁠. The sedenions are obtained by applying the Cayley–Dickson construction to the octonions, which can be mathematically expressed as ⁠ S = C D ( O , 1 ) {\displaystyle \mathbb {S} ={\mathcal {CD}}(\mathbb {O} ,1)} ⁠. As such, the octonions are isomorphic to a subalgebra of the sedenions. Unlike the octonions, the sedenions are not an alternative algebra. Applying the Cayley–Dickson construction to the sedenions yields a 32-dimensional algebra, called the trigintaduonions or sometimes the 32-nions. The term sedenion...

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