EXTENSIONS OF THE WITT ALGEBRA AND APPLICATIONS

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 paper is to give a classification of the extensions of the simple U-chi(W)-modules having p-character chi of height -1 <= r(chi) = 1 and r(chi) = p - 1 where p denotes the characteristic of the ground field. As an application we give a stronger proof of the wildness of U-chi(W) for -1 = r(chi) = 1 such that (r(chi), p) not equal (1, 5).