Topological Quantum Computation from non-abelian ... - Paul Fendley

The simplest kind of non-abelian statistics is in the braiding of Fibonacci anyons.Fusing two Fibonacci anyons gives a linear combination of a single Fibonacci anyon(denoted φ) and a state with trivial statistics (denoted 1). They satisfy the fusion ruleφ × φ ∼ 1 + φThis is like the tensor product of two spin-1 representations if we throw out the spin-2piece.The consistency rules governing braiding and fusing of anyons are identical to those of2d rational conformal field theory. These are known as the Moore-Seiberg axioms for auniversal modular tensor category.15