Equivariant Hochschild cohomology of group algebras and relative $\operatorname{Ext}$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866916031652429824 |
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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 |