ABSTRACT In this paper we generalize the concept of primitivation of monogenic functions taking values in a Clifford algebra, which is on its own a generalization to higher dimension of the primitivation problem for holomorphic functions in the complex plane. This problem can be stated as follows: given a monogenic function f(x0, x)f(x_0, \underline{x}) on \mathbbRm+1{\mathbb{R}}^{m+1} , i.e. a solution for the generalized Cauchy-Riemann operator D on \mathbbRm+1{\mathbb{R}}^{m+1} , construct a monogenic function g(x0, x)g(x_0, \underline{x}) such that [`(D)]g = f\overline{D}g = f . In view of the fact that, for monogenic functions g, this can be written as ¶x0\partial_{x_0} g = f, a straightforward generalization consists in replacing the scalar generator ¶x0\partial_{x_0} of translations in the x 0-direction by a generator of another transformation group. In this paper we consider translations in more dimensions.
