Higher Auslander Algebras of Finite Representation Type

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发表日期：

2026年1月24日

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Shen Li

摘要

Let $\Lambda $ $Λ$ be a higher Auslander algebra with global dimension $n+1$ $n + 1$ . In this paper, we prove that $\Lambda $ $Λ$ is representation-finite if and only if the number of non-isomorphic indecomposable $\Lambda $ $Λ$ -modules with projective dimension $n+1$ $n + 1$ is finite. As an application, we classify the representation-finite higher Auslander algebras of linearly oriented type $\mathbb {A}$ $A$ in the sense of Iyama and calculate the number of non-isomorphic indecomposable modules over these algebras.