Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.09496 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914972775219200 |
|---|---|
| author | Chen, Hui He, Jian Liu, Yu-Zhe |
| author_facet | Chen, Hui He, Jian Liu, Yu-Zhe |
| contents | The aim of this article is to study the Auslander algebra of any representation-finite string algebra. More precisely, we introduce the notion of gluing algebras and show that the Auslander algebra of a representation-finite string algebra is a quotient of a \gluing algebra of $\vec{A}^e_n $. As applications, the Auslander algebras of two classes of string algebras whose quivers are Dynkin types $A$ and $D$ are described. Moreover, the representation types of the above Auslander algebras are also given exactly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09496 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The tensorial description of the Auslander algebras of representation-finite string algebras Chen, Hui He, Jian Liu, Yu-Zhe Representation Theory The aim of this article is to study the Auslander algebra of any representation-finite string algebra. More precisely, we introduce the notion of gluing algebras and show that the Auslander algebra of a representation-finite string algebra is a quotient of a \gluing algebra of $\vec{A}^e_n $. As applications, the Auslander algebras of two classes of string algebras whose quivers are Dynkin types $A$ and $D$ are described. Moreover, the representation types of the above Auslander algebras are also given exactly. |
| title | The tensorial description of the Auslander algebras of representation-finite string algebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2410.09496 |