Let A be a commutative algebra over a field k, and VAbe the k-subalgebra of Endk(A) generated by EndA(A) = A and all k-derivations of A. A study of the homological properties of VAwas initiated by Hochschild, Kostant, and Rosenberg in [5], and continued by Rinehart [8], [9], Roos [11], Björk [1], Rinehart and Rosenberg [10], and others. It was proved in [5] that, if k is perfect and A is a regular affine algebra of dimension r, then the global dimension of VAis between r and 2r. Moreover, if k has positive characteristic, then gl.dim VA= 2r [8]. By a recent celebrated theorem of Roos [11], gl.dim VA= r if k has characteristic zero and A = k[x1, …, xr]; in this case VAis the so-called “Weyl algebra on 2r variables”.