algebra / Representation theory of algebras

The periodicity conjecture for finite-dimensional algebras

False: an explicit 36-dimensional algebra whose simple modules all have period four, but which has a 2-dimensional nonperiodic module and so is not itself periodic.

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algebraSep 9, 2026Significance 25/100Registry: unreviewed

The periodicity conjecture for finite-dimensional algebras

Prior state unknown→disproved

False: an explicit 36-dimensional algebra whose simple modules all have period four, but which has a 2-dimensional nonperiodic module and so is not itself periodic.

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False: an explicit 36-dimensional algebra whose simple modules all have period four, but which has a 2-dimensional nonperiodic module and so is not itself periodic.

False: an explicit 36-dimensional algebra whose simple modules all have period four, but which has a 2-dimensional nonperiodic module and so is not itself periodic.

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