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# Sedenions

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Sedenions are the 16-dimensional algebra obtained by applying the [Cayley-Dickson construction]? to the octonions.

Like octonions, multiplication? of sedenions is neither commutative nor associative. But unlike octonions, it does not 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

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

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Last edited August 11, 2001 3:45 am (diff)
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