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A counterexample to the periodicity conjecture for finite-dimensional algebras

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.09732

Author: Enomoto, Haruhisa

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7212135887

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