论文信息 - On the minimal extension and structure of weakly group-theoretical braided fusion categories

On the minimal extension and structure of weakly group-theoretical braided fusion categories

We show any slightly degenerate weakly group-theoretical fusion category admits a minimal extension. Let d be a positive square-free integer, given a weakly group-theoretical nondegenerate fusion category C, assume that FPdim(C) = nd and (n, d) = 1. If (FPdim(X), d) = 1 for all simple objects X of C, then we show that C contains a non-degenerate fusion subcategory C(Zd, q). In particular, we obtain that integral fusion categories of FP-dimensions pd such that C ⊆ sVec are nilpotent and group-theoretical, where p is a prime and (p, d) = 1.

Victor Ostrik | Zhiqiang Yu

[1] Michael Mueger. On the Structure of Modular Categories , 2002, math/0201017.

[2] P. Etingof,et al. Fusion categories and homotopy theory , 2009, 0909.3140.

[3] V. Drinfeld,et al. On braided fusion categories I , 2009, 0906.0620.

[4] S. Natale. The core of a weakly group-theoretical braided fusion category , 2017, 1704.03523.

[5] On fusion categories , 2002, math/0203060.

[6] Liang Kong,et al. Modular Extensions of Unitary Braided Fusion Categories and 2+1D Topological/SPT Orders with Symmetries , 2016, Communications in Mathematical Physics.

[7] Zhenghan Wang,et al. On the Classification of Weakly Integral Modular Categories , 2014, 1411.2313.

[8] V. Ostrik,et al. The Witt group of non-degenerate braided fusion categories , 2010, 1009.2117.

[9] P. Etingof,et al. WEAKLY GROUP-THEORETICAL AND SOLVABLE FUSION CATEGORIES , 2008, 0809.3031.

[10] Tobias J. Hagge,et al. Fermionic Modular Categories and the 16-fold Way , 2016, 1603.09294.

[11] V. Ostrik,et al. On the structure of the Witt group of braided fusion categories , 2011, 1109.5558.

[12] Z. Yu. On slightly degenerate fusion categories , 2019, Journal of Algebra.

[13] Nilpotent fusion categories , 2006, math/0610726.