On the Ringel--Hall algebra of the gentle one-cycle algebra $Λ(n-1,1,1)$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916116479082496 |
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| author | Chen, Hui Yang, Dong |
| author_facet | Chen, Hui Yang, Dong |
| contents | It is shown that the gentle one-cycle algebra $Λ(n-1,1,1)$ has Hall polynomials. The Hall polynomials are explicitly given for all triples of indecomposable modules, and as a consequence, the Ringel--Hall Lie algebra of $Λ(n-1,1,1)$ is shown to be isomorphic to its Riedtmann Lie algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03652 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Ringel--Hall algebra of the gentle one-cycle algebra $Λ(n-1,1,1)$ Chen, Hui Yang, Dong Representation Theory 16G20, 17B37 It is shown that the gentle one-cycle algebra $Λ(n-1,1,1)$ has Hall polynomials. The Hall polynomials are explicitly given for all triples of indecomposable modules, and as a consequence, the Ringel--Hall Lie algebra of $Λ(n-1,1,1)$ is shown to be isomorphic to its Riedtmann Lie algebra. |
| title | On the Ringel--Hall algebra of the gentle one-cycle algebra $Λ(n-1,1,1)$ |
| topic | Representation Theory 16G20, 17B37 |
| url | https://arxiv.org/abs/2402.03652 |