On slightly degenerate fusion categories

Boundary topological entanglement entropy in two and three dimensions

“…63-67, along with Ref. 68. Additionally, all multiplicity free fusion rings for ranks 1-6 can be found at Ref.…”

Group-Theoretical Property of Slightly Degenerate Fusion Categories of Certain Frobenius-Perron Dimensions

“…Since (D ad ) ′ =D pt by [2, Proposition 3.29], D ad can not pointed, particularly, D ad is not symmetric. While notice that if FPdim(D ad )=2p, 2q, 2p 2 or 2q 2 , then the M üger center of D ad is (D ad ) pt ∼ =D ′ =sVec, this is impossible, as D ad is slightly degenerate, which must be pointed by [9,Lemma 3.5].…”

“…If FPdim(D ad ) = 2p 2 q, then D pt ⊆ D ad and D pt contains a Tannakian category of Frobenius-Perron dimension q. In fact, if not, D pt ∼ = sVec⊠C(Z q ,η), then D ∼ = C(Z q ,η)⊠ C(Z q ,η) ′ C as braided fusion category, and D must be pointed by [9,Corollary 3.4]. Thus,…”

“…Recall that a braided fusion category C is said to be slightly degenerate, if its M üger center C ′ is braided equivalent to sVec, the category of finite-dimensional super vector spaces over K; while C is a non-degenerate fusion category if C ′ ∼ = Vec, the category of finite-dimensional vector spaces over K. In [9], the first named author studied slightly degenerate fusion categories of various Frobenius-Perron dimensions. In particular, for odd primes p and q, slightly degenerate fusion categories of Frobenius-Perron dimension 2p m q n d are always integral and solvable [9, Corollary 3.4, Proposition 3.14], where d is an odd square-free integer such that (pq,d) = 1.…”