The
Sedenions form a 16-dimensional
algebra over the
reals obtained by applying the [Cayley-Dickson construction]
? to the
octonions.
Like octonions, multiplication? of sedenions is neither commutative nor associative. Unlike octonions, it does not even have the property of being "alternative". Multiplication is alternative if:
- P(PQ) =(PP)Q
It does however have the property of being "power associative", since:
- PaPb = Pa+b
for
natural numbers a and
b.
The sedenions have multiplicative inverses, but they are not a division algebra. This is because they have "zero divisors", i.e. there exist non-zero sedenions P, Q such that:
- PQ = QP = 0
/Talk