[引用][C] Modular categories of Frobenius–Perron dimension and perfect modular categories
D Zhou, J Dong - International Journal of Mathematics, 2024 - World Scientific
D Zhou, J Dong
International Journal of Mathematics, 2024•World ScientificWe prove that modular categories of Frobenius–Perron dimension p 2 q 2 r 2 are solvable,
where p< q< r are prime numbers. As applications, we get that integral modular categories of
Frobenius–Perron dimension less than 1 8 0 0 are solvable, and hence integral perfect
modular categories have Frobenius–Perron dimension greater than or equal to 1 8 0 0.
When the modular categories considered are weakly group-theoretical, we further prove that
integral perfect modular categories have Frobenius–Perron dimension greater than or equal …
where p< q< r are prime numbers. As applications, we get that integral modular categories of
Frobenius–Perron dimension less than 1 8 0 0 are solvable, and hence integral perfect
modular categories have Frobenius–Perron dimension greater than or equal to 1 8 0 0.
When the modular categories considered are weakly group-theoretical, we further prove that
integral perfect modular categories have Frobenius–Perron dimension greater than or equal …
We prove that modular categories of Frobenius–Perron dimension are solvable, where are prime numbers. As applications, we get that integral modular categories of Frobenius–Perron dimension less than are solvable, and hence integral perfect modular categories have Frobenius–Perron dimension greater than or equal to . When the modular categories considered are weakly group-theoretical, we further prove that integral perfect modular categories have Frobenius–Perron dimension greater than or equal to .
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