Sedenions | |
---|---|
Symbol | |
Type | nonassociative algebra |
Units | e0, ..., e15 |
Multiplicative identity | e0 |
Main properties | power associativity distributivity |
Common systems | |
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 . They are obtained by applying the Cayley–Dickson construction to the octonions, and 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, sometimes called the 32-ions or trigintaduonions.[1] It is possible to continue applying the Cayley–Dickson construction arbitrarily many times.
The term sedenion is also used for other 16-dimensional algebraic structures, such as a tensor product of two copies of the biquaternions, or the algebra of 4 × 4 matrices over the real numbers, or that studied by Smith (1995).
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