0
votes
0answers
24 views

Is there a term for extending a finite magma by adding coefficients from fields?

For example, the Quaternion numbers at their base have the Cayley table: $ * = \begin{bmatrix} 1 & i & j & k \\ i & -1 & k & -j \\ j & -k & -1 & i \\ k & j ...
4
votes
1answer
110 views

Is there a name for a function whose square is an involution?

An involution is a function $f:X\to X$ such that $f\circ f=\text{id}$. Is there a name for a function $g:X\to X$ such that $f\equiv g\circ g$ is an involution? An example is multiplication by $\pm i$ ...
5
votes
1answer
250 views

Why do Quaternions and octonions exist?

Ok so I have known about imaginary numbers for quite some time now. I also understand why we want them to exist (to have a solution for $x^2=-1$). I also remember reading that the complex numbers are ...
2
votes
1answer
64 views

Is there a specific name and/or representation for the group of distinguishable orientations of a given shape?

Consider a 3-dimensional body $B$. The space of all orientations of $B$ in 3-space is the rotation group $SO(3)$, and is often represented in computer science applications as the quaternions with $q$ ...