Integrable derivations and stable equivalences of Morita type

TL;DR

This paper demonstrates that integrable derivations of symmetric algebras remain invariant under transfer maps induced by stable equivalences of Morita type, with implications for block theory over discrete valuation rings.

Contribution

It establishes the invariance of integrable derivations under transfer maps in Hochschild cohomology for symmetric algebras, extending to cases with unequal characteristic.

Findings

Integrable derivations are invariant under transfer maps.

Application to block theory over discrete valuation rings.

Connection between derivations and Hochschild cohomology Bockstein homomorphisms.

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.