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PreprintarXiv licencearXiv

A counterexample to the periodicity conjecture for finite-dimensional algebras

  • Haruhisa Enomoto
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Abstract

The periodicity conjecture asks whether a finite-dimensional algebra is periodic whenever all its simple modules are periodic. We construct a $36$-dimensional counterexample whose simple modules have period four. The algebra has a $2$-dimensional nonperiodic module, which shows that the algebra itself is not periodic.

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Cite

BibTeXRIS
BibTeX
@misc{enomoto2026counterexample,
  title = {{A counterexample to the periodicity conjecture for finite-dimensional algebras}},
  author = {Haruhisa Enomoto},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09732},
  eprint = {2609.09732},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09732},
}
RIS
TY  - UNPB
TI  - A counterexample to the periodicity conjecture for finite-dimensional algebras
AU  - Haruhisa Enomoto
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.09732
UR  - https://arxiv.org/abs/2609.09732
AB  - The periodicity conjecture asks whether a finite-dimensional algebra is periodic whenever all its simple modules are periodic. We construct a $36$-dimensional counterexample whose simple modules have period four. The algebra has a $2$-dimensional nonperiodic module, which shows that the algebra itself is not periodic.
ER  -