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ABSTRACT
Let G,H be groups, φ:G→H a group morphism, and A a G-graded algebra. The morphism φ 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.
Acknowledgment
The authors would like to thank Mariano Suárez-Álvarez for a careful reading of a previous version of this article.
Additional information
Funding
This work has been supported by the projects UBACYT 20020130 100533BA, pip-conicet 11220150100483CO, and MATHAMSUD-REPHOMOL. The first named author is a research member of CONICET (Argentina). The second named author is a FAPESP PostDoc Fellow, grant: 2016-25984-1 São Paulo Research Foundation (FAPESP).