Mutating ordered $τ$-rigid modules with applications to Nakayama algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917900840861696 |
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| author | Buan, Aslak B. Kaipel, Maximilian Terland, Håvard U. |
| author_facet | Buan, Aslak B. Kaipel, Maximilian Terland, Håvard U. |
| contents | A mutation operation for $τ$-exceptional sequences of modules over any finite-dimensional algebra was recently introduced, generalising the mutation for exceptional sequences of modules over hereditary algebras. We interpret this mutation in terms of TF-ordered $τ$-rigid modules, which are in bijection with $τ$-exceptional sequences. As an application we show that the mutation is transitive for Nakayama algebras, by providing an explicit combinatorial description of mutation over this class of algebras. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_13694 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mutating ordered $τ$-rigid modules with applications to Nakayama algebras Buan, Aslak B. Kaipel, Maximilian Terland, Håvard U. Representation Theory 16G20, 16G70, 18E40 A mutation operation for $τ$-exceptional sequences of modules over any finite-dimensional algebra was recently introduced, generalising the mutation for exceptional sequences of modules over hereditary algebras. We interpret this mutation in terms of TF-ordered $τ$-rigid modules, which are in bijection with $τ$-exceptional sequences. As an application we show that the mutation is transitive for Nakayama algebras, by providing an explicit combinatorial description of mutation over this class of algebras. |
| title | Mutating ordered $τ$-rigid modules with applications to Nakayama algebras |
| topic | Representation Theory 16G20, 16G70, 18E40 |
| url | https://arxiv.org/abs/2501.13694 |