Construction of simple non-weight sl(2)-modules of arbitrary rank

We study simple non-weight sl(2)-modules which are finitely generated as C[z]-modules. We show that they are described in terms of semilinear endomorphisms and prove that the Smith type induces a stratification on the set of these sl(2)-modules, providing thus new invariants. Moreover, we show that there is a notion of duality for these type of sl(2)-modules. Finally, we show that there are simple non-weight sl(2)-modules of arbitrary rank by constructing a whole new family of them.