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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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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. flexible.
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