A counterexample to the periodicity conjecture for finite-dimensional algebras
arXiv preprint, September 2026. Link: arXiv:2609.09732
Citation: H. Enomoto, A counterexample to the periodicity conjecture for finite-dimensional algebras, arXiv:2609.09732.
Comment
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.