Injective Hulls of Simple Modules Over Nilpotent Lie Color Algebras

TL;DR

This paper characterizes certain nilpotent Lie color algebras based on properties of their enveloping algebras' injective hulls of simple modules, using cocycle twists and grading techniques.

Contribution

It provides a new characterization of finite dimensional nilpotent Lie color algebras with locally Artinian injective hulls of simple modules via cocycle twists.

Findings

Characterization of nilpotent Lie color algebras with specific module properties

Connection between algebra gradings and module-theoretic properties

Results on gradings arising from the main characterization

Abstract

Using cocycle twists for associative graded algebras, we characterize finite dimensional nilpotent Lie color algebras $L$ graded by arbitrary abelian groups whose enveloping algebras $U(L)$ have the property that the injective hulls of simple right $U(L)$-modules are locally Artinian. We also collect together results on gradings on Lie algebras arising from this characterization.