Pre-modular fusion categories of small global dimensions (Q2118274)

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 \textit{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).