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

Abstract

The aim of this paper is to study the projective modules of the [Formula: see text]-reduced enveloping superalgebra [Formula: see text], where [Formula: see text] is the Lie superalgebra of superderivations on the Grassmann superalgebra [Formula: see text], over an algebraically closed field k of characteristic [Formula: see text]. Mainly, the Cartan invariants and the dimensions of indecomposable projective modules of [Formula: see text] are determined for any [Formula: see text]-character [Formula: see text] up to isomorphism.