Nakayama-type phenomena in higher Auslander--Reiten theory
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929256478539776 |
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| author | Jasso, Gustavo Külshammer, Julian |
| author_facet | Jasso, Gustavo Külshammer, Julian |
| contents | This paper surveys recent contructions in higher Auslander--Reiten theory. We focus on those which, due to their combinatorial properties, can be regarded as higher dimensional analogues of path algebras of linearly oriented type $\mathbb{A}$ quivers. These include higher dimensional analogues of Nakayama algebras, of the mesh category of type $\mathbb{Z}\mathbb{A}_\infty$ and the tubes, and of the triangulated category generated by an $m$-spherical object. For $m=2$, the latter category can be regarded as the higher cluster category of type $\mathbb{A}_\infty$ whose cluster-tilting combinatorics are controlled by the triangulations of the cylic apeirotope. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15889 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nakayama-type phenomena in higher Auslander--Reiten theory Jasso, Gustavo Külshammer, Julian Representation Theory This paper surveys recent contructions in higher Auslander--Reiten theory. We focus on those which, due to their combinatorial properties, can be regarded as higher dimensional analogues of path algebras of linearly oriented type $\mathbb{A}$ quivers. These include higher dimensional analogues of Nakayama algebras, of the mesh category of type $\mathbb{Z}\mathbb{A}_\infty$ and the tubes, and of the triangulated category generated by an $m$-spherical object. For $m=2$, the latter category can be regarded as the higher cluster category of type $\mathbb{A}_\infty$ whose cluster-tilting combinatorics are controlled by the triangulations of the cylic apeirotope. |
| title | Nakayama-type phenomena in higher Auslander--Reiten theory |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2402.15889 |