Pre-modular fusion categories of small global dimensions. (English) Zbl 1494.18014
The author prove the Lagrange theorem over global dimension of fusion categories (Theorem 3.1), which is a know result for Frobenius-Perron dimensions. The proof uses connected étale subalgebras. Then, classify premodular fusion categories of global dimension 6, 7, 8, 9 and 10 (Section 4), since for dimension less than or equal to 5 were classified by V. Ostrik [Contemp. Math. 728, 169–180 (2019; Zbl 1423.18023)]. Finally, the author shows that spherical fusion categories of global dimension 6 are weakly integral (Theorem 4.14).
Reviewer: Luz Adriana Mejia Castaño (Barranquilla)
MSC:
| 18M20 | Fusion categories, modular tensor categories, modular functors |
| 16T05 | Hopf algebras and their applications |
Citations:
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