Questions tagged [sedenions]
The sedenions are a 16 dimensional nonassociative algebra over the reals.
8
questions
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2answers
155 views
who pioneered the study of the sedenions?
The nature of this question is pure historical curiosity.
I found lots of background information about the discovery of both Imaginary and Complex Numbers, and enough information about the first two ...
3
votes
0answers
78 views
Java Library that supports Quaternions Octonions, Sedenions?
I would like to experiment with multi dimensional complex numbers such as quaternions octonions, sedenions.
I know Apache Commons Maths supports Quaternions, and I've found (although cannot download) ...
7
votes
2answers
359 views
Why do division algebras always have a number of dimensions which is a power of $2$?
Why do number systems always have a number of dimensions which is a power of $2$?
Real numbers: $2^0 = 1$ dimension.
Complex numbers: $2^1 = 2$ dimensions.
Quaternions: $2^2 = 4$ dimensions.
...
6
votes
0answers
170 views
Are complex split-octonions isomorphic to a more easily-defined algebra?
I write fiction and nonfiction, both which are mathy. My fiction is not usually supermathy but I'm working on a fictional story that has some math in it, and I prefer accuracy to mathbabble. I'm ...
31
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2answers
3k views
What specific algebraic properties are broken at each Cayley-Dickson stage beyond octonions?
I'm starting to come around to an understanding of hypercomplex numbers, and I'm particularly fascinated by the fact that certain algebraic properties are broken as we move through each of the $2^n$ ...
5
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3answers
588 views
Math beyond Quaternions
Quaternions remove the commutative property and octonions eliminate the associative property can we go any higher and eliminate more properties?
24
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2answers
3k views
Why are properties lost in the Cayley–Dickson construction?
Motivating question: What lies beyond the Sedenions?
I'm aware that one can construct a hierarchy of number systems via the Cayley–Dickson process:
$$\mathbb{R} \subset \mathbb{C} \subset \mathbb{H}...
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4answers
10k views
What lies beyond the Sedenions
In the construction of types of numbers, we have the following sequence:
$$\mathbb{R} \subset \mathbb{C} \subset \mathbb{H} \subset \mathbb{O} \subset \mathbb{S}$$
or:
$$2^0 \mathrm{-ions} \subset ...
