  Some unexpected properties of the cubic algebra generated by the covariant
derivatives of a generic Yang-Mills connection over the (s+1)-dimensional
pseudo Euclidean space are pointed out. This algebra is Gorenstein and Koszul
of global dimension 3 but except for s=1 (i.e. in the 2-dimensional case) where
it is the universal enveloping algebra of the Heisenberg Lie algebra and is a
cubic Artin-Schelter regular algebra, it fails to be regular in that it has
exponential growth. We give an explicit formula for the Poincare series of this
algebra A and for the dimension in degree n of the graded Lie algebra of which
A is the universal enveloping algebra.
  In the 4-dimensional (i.e. s=3) Euclidean case, a quotient of this algebra is
the quadratic algebra generated by the covariant derivatives of a generic
(anti) self-dual connection. This latter algebra is Koszul of global dimension
2 but is not Gorenstein and has exponential growth. It is the universal
enveloping algebra of the graded Lie-algebra which is the semi-direct product
of the free Lie algebra with three generators of degree one by a derivation of
degree one.
