# Questions tagged [non-associative-algebras]

Questions about non-associative algebras other than Lie algebras.

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### Finite dimensional real division algebra up to isotopy

Finite dimensional real division (non necessarily associative) algebras exist in dimensions 1, 2, 4, and 8. The standard example is a Hurwitz algebra $(A,*)$: reals, complexes, quaternions, octonions. ...
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### Combinatorics on non-associative words

In my P.h.d research, I deal (among other things) with non-associative words, which we call monomials, and we need to consider two types of operations with these monomials. The first one is simply ...
181 views

### Degree 8 multilinear operations on Jordan algebras

I am interested in the dimension, or, even better, in the $S_8$-module structure of the space of degree 8 multilinear operations on Jordan algebras. Recall that a Jordan algebra is a commutative but ...
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### Why is the automorphism group of the octonions $G_2$ instead of $SO(7)$

I can calculate the derivation of the octonions and I clearly find the 14 generators that form the algebra of $G_2$. However, when I do the same calculation for the quaternions, I end up with the ...
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### Separable nonassociative algebras

In his paper "Structure and Representation of Nonassociative Algebras", Schafer notes that an arbitrary nonassociative algebra over a field is separable "if and only if the ...
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### Conceptual meaning of the Dickson construction

The Cayley-Dickson construction (a.k.a. Dickson construction or Dickson doubling) constructs a new *-algebra $A'$ out of a given *-algebra $A$. As a vector space $A' = A \oplus A$, and the ...
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### Left- (right-) multiplications of an algebra that are derivations

Let us say that $A$ is a (finite-dimensional) algebra over a field of characteristic zero. We can assume commutativity but not associativity, if that makes it easier. Indeed, I am mostly interested in ...
755 views

### How many Lie and associative algebras over a finite field are there?

This question is related to the following general question: Given a variety of (non-associative) algebras $\mathcal V$, a finite field $\mathbb{F}_q$, with $q$ elements, and a positive integer $n$, ...