Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.05656 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909099078189056 |
|---|---|
| author | Sengupta, Annoy Kuber, Amit |
| author_facet | Sengupta, Annoy Kuber, Amit |
| contents | Generalising a recent work of Dequêne et al. on the connection between perfectly clustering words and band bricks over a particular family of gentle algebras, we characterise band bricks over string algebras whose underlying quiver is acyclic in terms of weakly perfectly clustering pairs of words -- a variant of perfectly clustering words. As a consequence, we characterise band semibricks over all such algebras. Furthermore, the combination of our result and a result of Mousavand and Paquette provides an algorithm to determine whether such a string algebra is brick-infinite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05656 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterisation of band bricks over certain string algebras and a variant of perfectly clustering words Sengupta, Annoy Kuber, Amit Representation Theory 16G20, 68R15 Generalising a recent work of Dequêne et al. on the connection between perfectly clustering words and band bricks over a particular family of gentle algebras, we characterise band bricks over string algebras whose underlying quiver is acyclic in terms of weakly perfectly clustering pairs of words -- a variant of perfectly clustering words. As a consequence, we characterise band semibricks over all such algebras. Furthermore, the combination of our result and a result of Mousavand and Paquette provides an algorithm to determine whether such a string algebra is brick-infinite. |
| title | Characterisation of band bricks over certain string algebras and a variant of perfectly clustering words |
| topic | Representation Theory 16G20, 68R15 |
| url | https://arxiv.org/abs/2402.05656 |