Sedenion

16-dimensional Cayley–Dickson algebra beyond the octonions: not even alternative, but still power-associative, and riddled with zero divisors.

Specifications & Metrics

type

Cayley–Dickson Algebras

symbol

S

Core Principles & Analysis

• Obtained by applying the Cayley–Dickson construction to the octonions, giving a 16-dimensional algebra.
• Multiplication is neither commutative nor associative, and in contrast to the octonions the sedenions are not even alternative.
• They retain power associativity, but unlike every algebra below them in the tower they contain zero divisors.

Sources

• Wikipedia: Sedenion