Behaviour of injective dimension with respect to regradings

ANDREA SOLOTAR; PABLO ZADUNAISKY

Bento Goncalves

Congreso; Lie and Jordan algebras, their representations and applications VI; 2015

Given a left noetherian $k$-algebra $A$ graded by a group $G$, an injective object $I$ inthe category of $G$-graded $A$-modules and a morphism from $G$ to another group $G´$, weprovide bounds for the injective dimension of $I$ as a $G´$-graded $A$-module. For this,we use three {em change of grading} functors. Most of the constructions concerning thesefunctors work in the context of $H$-comodule algebras, where $H$ is a Hopf algebra, so wedevelop them in this general context.