The Representation Type of the Descent Algebras of Type $\mathbb{A}$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909675205689344 |
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| author | Erdmann, Karin Lim, Kay Jin |
| author_facet | Erdmann, Karin Lim, Kay Jin |
| contents | We classify the representation type of the descent algebras of type $\A$ in the positive characteristic case. The algebras have finite representation type only for a few small degrees; otherwise, they are wild. Our main reduction method relies on a surjective algebra homomorphism from a descent algebra of type $\A$ to another of lower degree. For small degree cases, we employ techniques from the representation theory of finite-dimensional algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06471 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Representation Type of the Descent Algebras of Type $\mathbb{A}$ Erdmann, Karin Lim, Kay Jin Representation Theory 05E10, 20C30 We classify the representation type of the descent algebras of type $\A$ in the positive characteristic case. The algebras have finite representation type only for a few small degrees; otherwise, they are wild. Our main reduction method relies on a surjective algebra homomorphism from a descent algebra of type $\A$ to another of lower degree. For small degree cases, we employ techniques from the representation theory of finite-dimensional algebras. |
| title | The Representation Type of the Descent Algebras of Type $\mathbb{A}$ |
| topic | Representation Theory 05E10, 20C30 |
| url | https://arxiv.org/abs/2407.06471 |