A uniqueness property of τ exceptional sequences
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912117930590208 |
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| author | Hanson, Eric J. Thomas, Hugh |
| author_facet | Hanson, Eric J. Thomas, Hugh |
| contents | Recently, Buan and Marsh showed that if two complete $τ$-exceptional sequences agree in all but at most one term, then they must agree everywhere, provided the algebra is $τ$-tilting finite. They conjectured that the result holds without that assumption. We prove their conjecture. Along the way, we also show that the dimension vectors of the modules in a $τ$-exceptional sequence are linearly independent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_07118 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A uniqueness property of τ exceptional sequences Hanson, Eric J. Thomas, Hugh Representation Theory 16G20, 16G10 Recently, Buan and Marsh showed that if two complete $τ$-exceptional sequences agree in all but at most one term, then they must agree everywhere, provided the algebra is $τ$-tilting finite. They conjectured that the result holds without that assumption. We prove their conjecture. Along the way, we also show that the dimension vectors of the modules in a $τ$-exceptional sequence are linearly independent. |
| title | A uniqueness property of τ exceptional sequences |
| topic | Representation Theory 16G20, 16G10 |
| url | https://arxiv.org/abs/2302.07118 |