The G-centre and gradable derived equivalences
arXiv:1703.02623
Abstract
We propose a generalisation for the notion of the centre of an algebra in the setup of algebras graded by an arbitrary abelian group G. Our generalisation, which we call the G-centre, is designed to control the endomorphism category of the grading shift functors. We show that the G-centre is preserved by gradable derived equivalences given by tilting modules. We also discuss links with existing notions in superalgebra theory and apply our results to derived equivalences of superalgebras.
v2: extension to infinite groups; restriction on type of derived equivalence due to gap in proof of v1