The nilpotent generalized near-group fusion-ring conjecture

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Let C\mathcal{C} be a braided generalized near-group fusion category. Write R(m,n)R(m,n) for the corresponding generalized near-group fusion ring, with m,n∈Z≥1m,n\in\mathbb{Z}_{\geq 1}, and let KK be a finite abelian group. Nilpotent generalized near-group fusion-ring conjecture. If C\mathcal{C} is nilpotent, then the Grothendieck ring of C\mathcal{C} is isomorphic to

R(m,n)×ZKR(m,n)\times\mathbb{Z}K

for some m,n∈Z≥1m,n\in\mathbb{Z}_{\geq 1} and finite abelian group KK. The statement gives a proposed classification of the Grothendieck rings of nilpotent braided generalized near-group fusion categories; no resolution is supplied in the source.

References

Primary source

Andrew Schopieray, “Irrational braided generalized near-groups”, arXiv:2212.14009 (2022).

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