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arXiv · 2410.09496

The tensorial description of the Auslander algebras of representation-finite string algebras

Hui Chen·Jian He·Yu-Zhe Liu
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Abstract

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.

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BibTeXRIS

Hui Chen, Jian He, Yu-Zhe Liu. 2024-10-12. The tensorial description of the Auslander algebras of representation-finite string algebras. https://arxiv.org/abs/2410.09496

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