Indecomposable doubling for representations of the type I Lie superalgebras sl(m/n) and osp(2/2n)

TL;DR

This paper proves that for certain type I Lie superalgebras, each Kac module can be extended into a family of indecomposable modules, using explicit cohomology calculations.

Contribution

It introduces a new family of indecomposable modules for $sl(m/n)$ and $osp(2/2n)$, expanding the understanding of their representation theory.

Findings

Existence of a 1-parameter family of indecomposable extensions

Explicit cohomology calculations for these superalgebras

Extension of the module classification for type I Lie superalgebras

Abstract

We establish that for the type I Lie superalgebras $sl(m/n)$ and $osp(2/2n)$, each Kac module admits a 1 parameter family of indecomposable double extensions. The result follows from the explicit evaluation of the $H^1$ Lie superalgebra cohomology valued in the tensor product of the module and its dual.