A Bernstein-Gabber-Joseph theorem for affine algebras

Bernstein's famous result, that any non-zero module M over the n-th Weyl al gebra A(n) satisfies GKdim(M) greater than or equal to GKdim(A(n))/2, does not carry over to arbitrary simple affine algebras, as is shown by an examp le of McConnell. Bavula introduced the notion of filter dimension of simple algebra to explain this failure. Here, we introduce the faithful dimension of a module, a variant of the filter dimension, to investigate this phenom enon further and to study a revised definition of holonomic modules. We com pute the faithful dimension for certain modules over a variant of the McCon nell example to illustrate the utility of this new dimension. 1991 Mathemat ics subject classification: 16P90, 16P40, 16D60, 16S32.