Nahm Algebras

Abstract

Given a Lie algebra $\mathfrak{g}$, the \emph{Nahm algebra} of $\mathfrak{g}$ is the vector space $\mathfrak{g}\times \mathfrak{g}\times \mathfrak{g}$ 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.

23 pages, LaTeX2e, uses tcilatex.sty; submitted to J. Algebra