On solvability of the first Hochschild cohomology of odd p-groups
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914204322103296 |
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| author | Antrobus, Matthew |
| author_facet | Antrobus, Matthew |
| contents | We give a necessary and sufficient criterion for the solvability of $\operatorname{HH}^1(kP)$ as a Lie algebra, where $P$ is a $p$-group with $p$ odd, in terms of a directed graph constructed from the group $P$. This gives non-trivial results on the structure of such Lie algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14555 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On solvability of the first Hochschild cohomology of odd p-groups Antrobus, Matthew K-Theory and Homology Rings and Algebras Representation Theory 16E40 (Primary), 17B30 (Secondary) We give a necessary and sufficient criterion for the solvability of $\operatorname{HH}^1(kP)$ as a Lie algebra, where $P$ is a $p$-group with $p$ odd, in terms of a directed graph constructed from the group $P$. This gives non-trivial results on the structure of such Lie algebras. |
| title | On solvability of the first Hochschild cohomology of odd p-groups |
| topic | K-Theory and Homology Rings and Algebras Representation Theory 16E40 (Primary), 17B30 (Secondary) |
| url | https://arxiv.org/abs/2512.14555 |