Pre-modular fusion categories of global dimensions $p^2$

Publication date: 9 September 2022

Abstract: Let

p g e q 5

be a prime, we show that a non-pointed modular fusion category

m a t h c a l C

is Grothendieck equivalent to

m a t h c a l C (m a t h f r a k {s l}_{2}, 2 (p - 1))_{A}^{0}

if and only if

d i m (m a t h c a l C) = p c d o t u

, where

u

is a certain totally positive algebraic unit and

A

is the regular algebra of the Tannakian subcategory

e x t R e p (m a t h b b Z_{2}) s u b s e t e q m a t h c a l C (m a t h f r a k {s l}_{2}, 2 (p - 1))

. As a direct corollary, we classify non-simple modular fusion categories of global dimensions

p^{2}

.

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