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arXiv · 2610.22000

Classification of vanishing fusion rings of rank four

Jingcheng Dong·Sébastien Palcoux·Arnaud Plessis
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Abstract

A fusion ring is said to be vanishing if one of its multiplication matrices has determinant zero. We classify all vanishing fusion rings of rank four. We then provide a more explicit classification in the integral case, which allows us to derive several new consequences: there are infinitely many nonisomorphic simple integral vanishing fusion rings of rank four and no simple integral fusion ring of rank four is either $1$-Frobenius or Burnside.

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BibTeXRIS

Jingcheng Dong, Sébastien Palcoux, Arnaud Plessis. 2026-10-15. Classification of vanishing fusion rings of rank four. https://arxiv.org/abs/2610.22000

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