Extensions of simple modules for the Witt algebra

The irreducible representations of the Witt algebra $W$ are completely known. A classification of the irreducible $U_\chi(W)$--modules was first established by Chang and later simplified by Strade. The aim of this article is to give a classification of the extensions of the simple $U_\chi(W)$--modules having $p$--character $\chi$ of height $-1,0,1$ and $p-1$ where $p$ denotes the characteristic of the ground field.