Cartan invariants for the Witt superalgebra W(2) in positive characteristic

摘要

The aim of this paper is to study the projective modules of the chi-reduced enveloping superalgebra U-chi(W(2)), where W(n) is the Lie superalgebra of superderivations on the Grassmann superalgebra Lambda(n), over an algebraically closed field k of characteristic p > 2. Mainly, the Cartan invariants and the dimensions of indecomposable projective modules of U-chi(W(2)) are determined for any p-character chi up to isomorphism.