Representation theory of hereditary artin algebras of finite representation type

2025/06/28 by Shiping Liu, Gordana Todorov, Liu, Shiping +1
Mathematics · #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2506.22987

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 \mathscrC_H, as well as the nilpotencies of the radicals of \mmod H\hspace-.4pt, \hspace-.5pt D^\hspace.5ptb\hspace-.6pt(\hspace-.5pt\mmod H\hspace-.5pt) and \mathscrC_H.

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