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THE $G$-CENTRE AND GRADABLE DERIVED EQUIVALENCES

Part of: Abelian categories Modules, bimodules and ideals General and miscellaneous

Published online by Cambridge University Press:  18 June 2018

KEVIN COULEMBIER  and
VOLODYMYR MAZORCHUK
KEVIN COULEMBIER*
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia email [email protected]
VOLODYMYR MAZORCHUK
Affiliation:
Department of Mathematics, University of Uppsala, Box 480, SE-75106, Uppsala, Sweden email [email protected]
*
✉[email protected]
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Abstract

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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.

Keywords

group actionsgradingsderived equivalencesgeneralisations of centressuperalgebras

MSC classification

Primary: 16B50: Category-theoretic methods and results (except as in )
Secondary: 16D90: Module categories ; module theory in a category-theoretic context; Morita equivalence and duality 18E30: Derived categories, triangulated categories
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 105 , Issue 3 , December 2018 , pp. 289 - 315
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

K.C. is supported by Australian Research Council Discover-Project Grant DP140103239. V.M. is supported by the Swedish Research Council and the Göran Gustafssons Foundation.

References

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