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 or blackboard bold .
Key facts
- Number system.official_name
- Sedenions
- Number system.symbol
- \mathbb S
- Number system.type
- Hypercomplex algebra
- Number system.units
- e0, ..., e15
- Number system.identity
- e0
- Number system.hide_common
- true
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- Sedenion-Fano Tesseract.gif
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- Sedenions
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Article
11 sectionsContents
- Arithmetic
- Multiplication
- Sedenion properties
- Anti-associative
- Quaternionic subalgebras
- Zero divisors
- Space of Zero Divisors
- Applications
- See also
- Notes
- References
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 or blackboard bold .
The sedenions are obtained by applying the Cayley–Dickson construction to the octonions, which can be mathematically expressed as {{tmath|1= \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.