Hui Chen, Jian He, Yu-Zhe Liu
Published 2024-10-12Version 1
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.
Classifying $τ$-tilting modules over the Auslander algebra of $K[x]/(x^n)$
Exceptional sequences and spherical modules for the Auslander algebra of $k[x]/(x^t)$
On the number of tilting modules over a class of Auslander algebras
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