Nahm Algebras

Details Nahm Algebras Nahm Algebras

1999-07-13

arxiv.org/abs/math/9907084v1

J. Algebra 247 (2002), no. 2, 269--294.

Mathematics

Rings and Algebras

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

Scientific paper

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.

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