Mutation of $τ$-exceptional sequences for acyclic quivers over local algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909722647461888 |
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| author | Nonis, Iacopo |
| author_facet | Nonis, Iacopo |
| contents | Let $k$ be an algebraically closed field. Let $R$ be a local commutative finite dimensional $k$-algebra and let $Q$ be a quiver with no loops or oriented cycles. We show that mutation of $τ$-exceptional sequences over $Λ= R\otimes_k kQ \cong RQ$ in the sense of Buan, Hanson, and Marsh coincides with the classical mutation of exceptional sequences defined by Crawley-Boevey and Ringel. In particular, the braid group acts transitively on the set of complete $τ$-exceptional sequences in $\text{mod }Λ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22770 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mutation of $τ$-exceptional sequences for acyclic quivers over local algebras Nonis, Iacopo Representation Theory 16D90, 16G10, 16G20, 16S90 Let $k$ be an algebraically closed field. Let $R$ be a local commutative finite dimensional $k$-algebra and let $Q$ be a quiver with no loops or oriented cycles. We show that mutation of $τ$-exceptional sequences over $Λ= R\otimes_k kQ \cong RQ$ in the sense of Buan, Hanson, and Marsh coincides with the classical mutation of exceptional sequences defined by Crawley-Boevey and Ringel. In particular, the braid group acts transitively on the set of complete $τ$-exceptional sequences in $\text{mod }Λ$. |
| title | Mutation of $τ$-exceptional sequences for acyclic quivers over local algebras |
| topic | Representation Theory 16D90, 16G10, 16G20, 16S90 |
| url | https://arxiv.org/abs/2505.22770 |