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Let g be the finite dimensional Witt algebra W(1,1) over an algebraicallyclosed field of characteristic p > 3. It is well known that all simpleW(1,1)-modules are finite dimensional. Each simple module admits a character\chi in g^*. Given such a \chi one can form the (finite dimensional) reducedenveloping algebra u(g,\chi). The simple modules for u(g,\chi) are preciselythose simple W(1,1)-modules admitting the character \chi. In this paper theauthors compute Ext^1 between pairs of simple modules for u(g,\chi).

Ext^1-quivers for the Witt algebra W(1,1)