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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.13038 |
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| _version_ | 1866912648188133376 |
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| author | Martínez-Pérez, Conchita Mendonça, Luis |
| author_facet | Martínez-Pérez, Conchita Mendonça, Luis |
| contents | We characterize in terms of a combinatorial condition on the graph $Γ$ when the group $\mathrm{PAut}(A_Γ)$ of pure symmetric automorphisms of the RAAG $A_Γ$ and its outer version $\mathrm{POut}(A_Γ)$ have a descending central Lie algebra which is Koszul. To do that, we prove that our combinatorial condition implies that these groups are iterated extensions of RAAGs; in particular, they are poly-free. On the other hand, we show that $\mathrm{PAut}(F_n)$ is not poly-finitely generated free for $n \geq 4$. We also show that groups in a certain class containing $\mathrm{PAut}(A_Γ)$ are 1-formal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13038 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pure symmetric automorphisms, extensions of RAAGs, and Koszulness Martínez-Pérez, Conchita Mendonça, Luis Group Theory Rings and Algebras We characterize in terms of a combinatorial condition on the graph $Γ$ when the group $\mathrm{PAut}(A_Γ)$ of pure symmetric automorphisms of the RAAG $A_Γ$ and its outer version $\mathrm{POut}(A_Γ)$ have a descending central Lie algebra which is Koszul. To do that, we prove that our combinatorial condition implies that these groups are iterated extensions of RAAGs; in particular, they are poly-free. On the other hand, we show that $\mathrm{PAut}(F_n)$ is not poly-finitely generated free for $n \geq 4$. We also show that groups in a certain class containing $\mathrm{PAut}(A_Γ)$ are 1-formal. |
| title | Pure symmetric automorphisms, extensions of RAAGs, and Koszulness |
| topic | Group Theory Rings and Algebras |
| url | https://arxiv.org/abs/2510.13038 |