Questions tagged [sedenions]
The sedenions are a 16 dimensional nonassociative algebra over the reals.
9
questions
1
vote
1
answer
36
views
Is division by a null sedenion a valid operation?
So octonion set provides the largest normed division algebra, and starting with sedenions, Cayley-Dickson construction provides algebras with zero divisors.
From what I understand, it means there are ...
2
votes
2
answers
199
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
0
answers
104
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
2
answers
414
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
0
answers
181
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 ...
33
votes
2
answers
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 $2^n$ ...
4
votes
3
answers
654
views
Math beyond Quaternions
Quaternions remove the commutative property and octonions eliminate the associative property can we go any higher and eliminate more properties?
26
votes
2
answers
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:
$$\mathbb{R} \subset \mathbb{C} \subset \mathbb{H}...
61
votes
4
answers
11k
views
What lies beyond the Sedenions
In the construction of types of numbers, we have the following sequence:
$$\mathbb{R} \subset \mathbb{C} \subset \mathbb{H} \subset \mathbb{O} \subset \mathbb{S}$$
or:
$$2^0 \mathrm{-ions} \subset ...