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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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