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arXiv · 2506.22987

Representation theory of hereditary artin algebras of finite representation type

Shiping Liu·Gordana Todorov
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Abstract

Let $H$ be a hereditary artin algebra of finite representation type. We first determine all hammocks in the Auslander-Reiten quiver $\GaH$ of $\mmod H$, the category of finitely generated left $H$-modules. This enables us to obtain an effective method to construct $\GaH$ by simply viewing the ext-quiver of $H$. As easy applications, we compute the numbers of non-isomorphic indecomposable objects in $\mmod H$ and the associated cluster category $\mathscr{C}_H$, as well as the nilpotencies of the radicals of $\mmod H\hspace{-.4pt},$ $\hspace{-.5pt} D^{\hspace{.5pt}b\hspace{-.6pt}}(\hspace{-.5pt}\mmod H\hspace{-.5pt})$ and $\mathscr{C}_H$.

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BibTeXRIS

Shiping Liu, Gordana Todorov. 2025-06-28. Representation theory of hereditary artin algebras of finite representation type. https://arxiv.org/abs/2506.22987

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