Abstract
Recall that the goal of representation theory is to classify the indecomposable modules and the morphisms between them. The Auslander–Reiten quiver is a first approximation of the module category. If the quiver is of finite representation type, then the Auslander–Reiten quiver gives a complete picture of the module category.
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Schiffler, R. (2014). Auslander–Reiten Theory. In: Quiver Representations. CMS Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-09204-1_7
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DOI: https://doi.org/10.1007/978-3-319-09204-1_7
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