Nahm Algebras

Given a Lie algebra $\frak{g}$, the \emph{Nahm algebra} of $\frak{g}$ is the vector space $\frak{g}\times \frak{g}\times \frak{g}$ with the natural commutative, nonassociative algebra structure associated with the Nahm equations $\dot{x} = [y,z]$, $\dot{y} = [z,x]$, $\dot{z} = [x,y]$. Motivated by potential application to the study of these equations, we herein initiate the study of Nahm algebras.