Total preprojective algebras
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912755212091392 |
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| author | Chan, Aaron Iyama, Osamu Marczinzik, Rene |
| author_facet | Chan, Aaron Iyama, Osamu Marczinzik, Rene |
| contents | We introduce total preprojective algebras $Ψ$ of path algebras of Dynkin quivers $kQ$, and prove that they are isomorphic to $2$-Auslander algebras of preprojective algebras $Π$ of $kQ$. In particular, $Ψ$ has global dimension $3$ and dominant dimension $3$. We also describe $Ψ$ as a tensor algebra of a certain explicit bimodule over the Auslander algebra of $kQ$. As an application, we give a presentation of $Ψ$ by explicit quivers with relations. More generally, we introduce total $(d+1)$-preprojective algebras of $d$-representation finite algebras, and give all the corresponding results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04683 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Total preprojective algebras Chan, Aaron Iyama, Osamu Marczinzik, Rene Representation Theory 16G10 We introduce total preprojective algebras $Ψ$ of path algebras of Dynkin quivers $kQ$, and prove that they are isomorphic to $2$-Auslander algebras of preprojective algebras $Π$ of $kQ$. In particular, $Ψ$ has global dimension $3$ and dominant dimension $3$. We also describe $Ψ$ as a tensor algebra of a certain explicit bimodule over the Auslander algebra of $kQ$. As an application, we give a presentation of $Ψ$ by explicit quivers with relations. More generally, we introduce total $(d+1)$-preprojective algebras of $d$-representation finite algebras, and give all the corresponding results. |
| title | Total preprojective algebras |
| topic | Representation Theory 16G10 |
| url | https://arxiv.org/abs/2502.04683 |