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

2024/10/12 by Chen, Hui, He, Jian, Liu, Yu-Zhe
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2410.09496

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 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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