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| Title of object: |
flexible algebra |
| Canonical Name: |
FlexibleAlgebra |
| Type: |
Definition |
| Created on: |
2004-10-10 14:34:05 |
| Modified on: |
2006-01-26 21:19:59 |
| Classification: |
msc:17A20 |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb,amscd}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here |
Content:
| A non-associative algebra $A$ is \emph{flexible} if $[\ a,b,a\ ]=0$ for all $a,b\in A$, where $[\ , , ]$ is the associator on $A$. In other words, we have $(ab)a=a(ba)$ for all $a,b\in A$. Any associative algebra is clearly flexible. Furthermore, any alternative algebra with characteristic $\neq 2$ is flexible. |
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