Anyons is the generic name for the particles which interchange among other according to the representation(s) of the braid group.

The braid group is the group describing exchange of object in two-space dimensions, when knot between trajectories can happen.

One mainly distinguish between the Abelian and non-Abelian Anyons. The Abelian Anyons exchange is described by the uni-dimensional representation of the braiding group, whereas non-Abelian Anyons exchange is described by higher-dimensional representation(s) of the braiding group.

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