Skip to main content

All Questions

Filter by
Sorted by
Tagged with
1 vote
0 answers
76 views

What is the operator norm of the sedenions and beyond?

Suppose that $K$ is a field. Then for all $n$, define a bilinear operation $*$ (or $*_{n,K}$ in case there may be ambiguity) on $K^{2^n}$ along with a conjugation operation $^*$ on $K^{2^n}$ by ...
Joseph Van Name's user avatar
4 votes
1 answer
686 views

Who and when proved Artin's Theorem on alternative rings?

I am interested in the history of the proof of Artin's Theorem (on the diassociativity of alternative rings). Question. When has Artin proved this theorem and where was it published for the first ...
Taras Banakh's user avatar
  • 41.8k
3 votes
0 answers
89 views

Non-associative algebras and determinant over 3 by 3 matrices

I have a non associative algebra $A$ that is not unital. And I have three by three matrices $X$ with coefficients over $A$ with a matrix product $*$. I'd like to define something like the determinant ...
Dac0's user avatar
  • 295
10 votes
1 answer
807 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 $n$, ...
Thiago's user avatar
  • 398
3 votes
0 answers
134 views

Language representation problem regarding non-commutative, non-associative algebras

Consider a sentence as a series of words with an associated set of labels that tell one how information is passed through the sentence - examples include combinatory categorical grammars or Lambek ...
East's user avatar
  • 149