  In this article we present some probably unexpected (in our opinion)
properties of representations of Yang-Mills algebras. We first show that any
free Lie algebra with m generators is a quotient of the Yang-Mills algebra
ym(n) on n generators, for n greater than or equal to 2m. We derive from this
that any semisimple Lie algebra, and even any affine Kac-Moody algebra is a
quotient of ym(n), for n greater than or equal to 4. Combining this with
previous results on representations of Yang-Mills algebras given in an article
by the author together with A. Solotar, one may obtain solutions to the
Yang-Mills equations by differential operators acting on sections of twisted
vector bundles on the affine space associated to representations of any
semisimple Lie algebra. We also show that this quotient property does not hold
for n = 3, since any morphism of Lie algebras from ym(3) to sl(2,k) has in fact
solvable image.
