 This bundle has a natural "right" action determined by
where "v" is a differential operator of order one, that is to say a vector field, ω a "n"-form ("n" = dim "X"), and Lie denotes the Lie derivative.Locally, after choosing some system of coordinates "x"1, ..., "x""n" ("n" = dim "X") on "X", which determine a basis ∂1, ..., ∂"n" of the tangent space of "X", sections of "D""X" can be uniquely represented as expressions
In particular, when "X" is the "n"-dimensional affine space, this "D""X" is the Weyl algebra in "n" variables.Many basic properties of "D"-modules are local and parallel the situation of coherent sheaves.