  Classical W-algebras in higher dimensions have been recently constructed. In
this letter we show that there is a finitely generated subalgebra which is
isomorphic to the algebra of local diffeomorphisms in D dimensions. Moreover,
there is a tower of infinitely many fields transforming under this subalgebra
as symmetric tensorial one-densities. We also unravel a structure isomorphic to
the Schouten symmetric bracket, providing a natural generalization of w_\infty
in higher dimensions.
