# Questions tagged [sedenions]

The sedenions are a 16 dimensional nonassociative algebra over the reals.

14 questions
Filter by
Sorted by
Tagged with
56 views

### Closed form of product of sedenions

I'm a math student and I'm taking an algebra course. The professor introduced us to the field of quaternions ($\mathbb{Q}$), I became very curious about the topic and I saw that in addition to ...
946 views

### Does the $32$-inator exist?

Background It is common popular-math knowledge that as we extend the real numbers to complex numbers, quaternions, octonions, sedenions, $32$-nions, etc. using the Cayley-Dickson construction, we lose ...
• 5,791
186 views

### Norm of the Sedenions

Let the Cayley-Dickson doubling of the octonions be called the sedenions. The sedenions are not a division algebra, because they contain zero divisors. The presence of zero divisors means that the ...
• 283
71 views

### Multiplication identities of Cayley-Dickson algebras after the sedenions

Consider the multiplication reducts $\{*\}$ of Cayley-Dickson algebras $(X;+,-,*,0,1)$ over the real numbers $\mathbb{R}$. In both the real numbers and the complex numbers, multiplication satisfies ...
• 20.2k
1 vote
56 views

### What comes in the next several K-D steps after the sedenions, and what is lost?

Wikipedia and elsewhere seem to say that one can keep on extrapolating forever in hypercomplexification, but that you progressively lose operation-equative symetries or whatever you call, e.g. ...
102 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 ...
• 123
268 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 ...
131 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) ...
• 219
513 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. ...
• 822
200 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 ...
• 293
4k 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 $2^n$ ...
• 691
853 views

### Math beyond Quaternions

Quaternions remove the commutative property and octonions eliminate the associative property can we go any higher and eliminate more properties?
• 179