Questions tagged [nonassociative-algebras]
65 questions
5
votes
1 answer
Zorn vector-matrix description of octonion multiplication
Zorn's vector-matrices are a way to describe split octonions by treating them as matrices
$$ \begin{bmatrix}a & \mathbf v\\ \mathbf w & b\end{bmatrix} $$
where $a,b \in \mathbb{R}$ and $\mathbf{v}, \mathbf{w} \in \mathbb{R}^3$. The multiplication…
John Baez
- 1,648
1
vote
0 answers
Polynomial alternative algebra
Let $F[x]$ be an polynomial alternative algebra over a field $F$. How I compute the universal multiplication envelope of $F[x]$?
Gabriel G
- 47
0
votes
0 answers
Representation of Lie triple systems
While reading the definition of a representation of a Lie triple system, I have a few doubts which I have stated at the end.
Let $(T, \{\cdot,\cdot,\cdot\})$ be a Lie triple system and $V$ be a vector space along with a linear map $\theta: T \otimes…
Saikat
- 1,583
0
votes
0 answers
Given an alternative algebra A, is the algebra generated by two commutative, associative subalgebras B and C always associative?
The algebras are over a field.
The answer to the question is yes when B and C are generated by 1 element each. Over the octonions, the answer to the question is then yes. What about in general?
wlad
- 8,185
0
votes
1 answer
What kind of algebra and how can I learn its properties
I try to find any information on the following algebra defined as:
$$(a,b)+(c,d)=(a+c,b+d)$$
$$(a,b)*(c,d)=(ac,ac-bd)$$
It is non-associative, but commutative and distributive.
Can it be classified somehow? Do there exist any information on it? How…
oddy
- 51