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| Classification of Certain Weakly IntegralFusion Categories |
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Citation： |
Jingcheng DONG.Classification of Certain Weakly IntegralFusion Categories[J].Chinese Annals of Mathematics B,2026,(3):555~572 |
| Page view： 97
Net amount： 47 |
Authors： |
Jingcheng DONG; |
Foundation： |
the Natural Science Foundation of Jiangsu Province (No. BK20201390) |
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| Abstract： |
The author proves that braided fusion categories of Frobenius-Perron dimension
pmqnd or p2q2r2 are weakly group-theoretical, where p, q, r are distinct prime numbers, d
is a square-free natural number such that (pq, d) = 1. As an application, the author
obtains that weakly integral braided fusion categories of Frobenius-Perron dimension less
than 1800 are weakly group-theoretical, and weakly integral braided fusion categories of
odd dimension less than 33075 are solvable. For the general case, the author proves that
fusion categories (not necessarily braided) of Frobenius-Perron dimension 84 and 90 are
either solvable or group-theoretical. Together with the results in the literature, this shows
that every weakly integral fusion category of Frobenius-Perron dimension less than 120
is either solvable or group-theoretical. Thus the author completes the classification of all
these fusion categories in terms of Morita equivalence. |
Keywords： |
Solvable fusion categories Group-theoretical fusion categories Weakly
group-theoretical fusion categories Frobenius property |
Classification： |
18M20, 18M15 |
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