A field guide to categories with $A_n$ fusion rules

Abstract

We collate information about the fusion categories with $A_n$ fusion rules. This note includes the classification of these categories, a realisation via the Temperley-Lieb categories, the auto-equivalence groups (both braided and tensor), identifications of the subcategories of invertible objects, and explicit descriptions of the Drinfeld centres. The first section describes the classification of these categories (as monoidal, dagger, pivotal, and braided categories). The second section describes the properties of these categories.

References in corpus (6)

• Applications of braided endomorphisms from conformal inclusions
• Skein theory for the D_{2n} planar algebras
• The center functor is fully faithful
• On braided fusion categories I
• A minus sign that used to annoy me but now I know why it is there
• The Brauer-Picard groups of the fusion categories coming from the $ADE$ subfactors

Cited by in corpus (1)

• Composing topological domain walls and anyon mobility