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arXiv · 2610.41527

Composition factor algebras and finite representation type

Bo Le·Bin Zhu
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Abstract

An Artin algebra is called a composition factor algebra if its indecomposable finitely generated modules are determined, up to isomorphism, by their composition factors. We prove that every composition factor algebra is representation-finite. This settles a conjecture of Auslander, Reiten and Smalø. We also give criteria for comma categories and factorization categories to be of finite representation type.

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Bo Le, Bin Zhu. 2026-10-30. Composition factor algebras and finite representation type. https://arxiv.org/abs/2610.41527

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