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arXiv · 2308.10433

Higher Auslander algebras of finite representation type

Shen Li
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Abstract

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

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Shen Li. 2023-08-21. Higher Auslander algebras of finite representation type. https://arxiv.org/abs/2308.10433

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