Equivariant Hochschild cohomology of group algebras and relative $\operatorname{Ext}$

Fuente: arXiv
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Auteurs principaux: Pojar, Andrada, Todea, Constantin-Cosmin
Format: Preprint
Publié: 2026
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author Pojar, Andrada
Todea, Constantin-Cosmin
author_facet Pojar, Andrada
Todea, Constantin-Cosmin
contents For a finite group $Γ$, acting on a finite group $G,$ we find necessary conditions for which the first $Γ_0$-equivariant Hochschild cohomology of the group algebra $kG$ is non-trivial, where $k$ is a field of characteristic $p$ dividing the order of $G$ and $Γ_0$ is the stabilizer subgroup in $Γ$ of some element in $G.$ For any field $k$ we show that the $Γ$-equivariant Hochschild cohomology of $Γ$-algebras with coefficients in a $Γ$-equivariant bimodule (Jensen, 1996) is isomorphic with some $kΓ$-relative $\operatorname{Ext},$ in the context of relative homological algebra.
format Preprint
id arxiv_https___arxiv_org_abs_2605_10733
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Equivariant Hochschild cohomology of group algebras and relative $\operatorname{Ext}$
Pojar, Andrada
Todea, Constantin-Cosmin
K-Theory and Homology
16E40, 20J06
For a finite group $Γ$, acting on a finite group $G,$ we find necessary conditions for which the first $Γ_0$-equivariant Hochschild cohomology of the group algebra $kG$ is non-trivial, where $k$ is a field of characteristic $p$ dividing the order of $G$ and $Γ_0$ is the stabilizer subgroup in $Γ$ of some element in $G.$ For any field $k$ we show that the $Γ$-equivariant Hochschild cohomology of $Γ$-algebras with coefficients in a $Γ$-equivariant bimodule (Jensen, 1996) is isomorphic with some $kΓ$-relative $\operatorname{Ext},$ in the context of relative homological algebra.
title Equivariant Hochschild cohomology of group algebras and relative $\operatorname{Ext}$
topic K-Theory and Homology
16E40, 20J06
url https://arxiv.org/abs/2605.10733