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Integrable Derivations and Stable Equivalences of Morita Type

Part of: Representation theory of rings and algebras Homological methods Modules, bimodules and ideals

Published online by Cambridge University Press:  15 February 2018

Markus Linckelmann
Markus Linckelmann*
Affiliation:
Department of Mathematics, City, University London, Northampton Square, London EC1V 0HB, UK (markus.linckelmann.1@city.ac.uk)
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Abstract

Using that integrable derivations of symmetric algebras can be interpreted in terms of Bockstein homomorphisms in Hochschild cohomology, we show that integrable derivations are invariant under the transfer maps in Hochschild cohomology of symmetric algebras induced by stable equivalences of Morita type. With applications in block theory in mind, we allow complete discrete valuation rings of unequal characteristic.

Keywords

derivationstable equivalence

MSC classification

Primary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) 16G30: Representations of orders, lattices, algebras over commutative rings 16D90: Module categories ; module theory in a category-theoretic context; Morita equivalence and duality
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 2 , May 2018 , pp. 343 - 362
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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