Trivial Sector: Trivial

Trivial is the trivial sector for ordinary vector spaces. It is the trivial representation of the trivial group, equivalently Rep[ℤ₁].

Sector type

TensorKitSectors.TrivialType
struct Trivial <: Sector
Trivial()

Singleton type to represent the trivial sector, i.e. the trivial representation of the trivial group. This is equivalent to Rep[ℤ₁], or the unit object of the category Vect of ordinary vector spaces.

source

There is only one label:

using TensorKitSectors

Trivial()

Fusion Rules

Fusion is uniquely trivial:

\[1 \otimes 1 = 1.\]

Therefore FusionStyle(Trivial) = UniqueFusion() and Nsymbol(Trivial(), Trivial(), Trivial()) == true.

Topological Data

The quantum dimension is 1. fusiontensor is a 1 × 1 × 1 × 1 array containing 1. The associator and braiding are both trivial:

\[F = 1,\qquad R = 1.\]

The braiding style is Bosonic().

References