Injective hulls of simple modules over finite dimensional nilpotent complex Lie superalgebras

TL;DR

This paper characterizes finite dimensional nilpotent complex Lie superalgebras based on the local Artinian property of injective hulls of their simple modules, identifying specific structural conditions on their even parts.

Contribution

It provides a precise classification of nilpotent Lie superalgebras whose simple module injective hulls are locally Artinian, linking module-theoretic properties to algebraic structure.

Findings

Characterization of Lie superalgebras with locally Artinian injective hulls

Identification of structural conditions on the even part g_0

Explicit description of specific nilpotent Lie algebras involved

Abstract

We show that the finite dimensional nilpotent complex Lie superalgebras g whose injective hulls of simple U(g)-modules are locally Artinian are precisely those whose even part g_0 is isomorphic to a nilpotent Lie algebra with an abelian ideal of codimension 1 or to a direct product of an abelian Lie algebra and a certain 5-dimensional or a certain 6-dimensional nilpotent Lie algebra.