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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{le2026composition,
  title = {{Composition factor algebras and finite representation type}},
  author = {Bo Le and Bin Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41527},
  eprint = {2610.41527},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41527},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Composition factor algebras and finite representation type
AU  - Bo Le
AU  - Bin Zhu
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41527
UR  - https://arxiv.org/abs/2610.41527
AB  - 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.
ER  -