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THE $G$-CENTRE AND GRADABLE DERIVED EQUIVALENCES
Part of
KEVIN COULEMBIER, VOLODYMYR MAZORCHUK
Journal:

Journal of the Australian Mathematical Society / Volume 105 / Issue 3 / December 2018

Published online by Cambridge University Press:

18 June 2018, pp. 289-315

Print publication:

December 2018
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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.