Classification of vanishing fusion rings of rank four
Jingcheng Dong, Sébastien Palcoux, Arnaud Plessis
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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