Injective Hulls of Simple Modules Over Nilpotent Lie Color Algebras

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.

A section on gradings on finite dimensional nilpotent Lie algebras of almost maximal index has been added and some minor changes have been made

References in corpus (2)

• Injective Modules over Down-Up Algebras
• Injective hulls of simple modules over finite dimensional nilpotent complex Lie superalgebras