2015•Journal of Algebra and Its ApplicationsRequires access

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

Feifei Duan, Fang Li

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.

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Key concepts: Algebraically closed field, Superalgebra, Mathematics, Lie superalgebra, Indecomposable module, Pure mathematics, Isomorphism (crystallography), Field (mathematics)