Change of grading, injective dimension and dualizing complexes

摘要

Let G,H be groups, phi : G - Ha group morphism, and A a G-graded algebra. The morphism phi induces an H-grading on A, and on any G-graded A-module, which thus becomes an H-graded A-module. Given an injective G-graded A-module, we give bounds for its injective dimension when seen as H-graded A-module. Following ideas by Van den Bergh, we give an application of our results to the stability of dualizing complexes through change of grading.