An algebraic framework for characterizing topological orders in two-dimensional systems is presented by combining the braid group formalism with a gauge invariance analysis. We show that flux insertions (or large gauge transformations) pertinent to the toroidal topology induce automorphisms of the braid group.
At least in the abelian cases, this results in a unified algebraic structure that characterizes both the ground-state subspace and fractionally charged, anyonic quasiparticles, without assuming any relation between quasiparticle charge and statistics. We also discuss possible ways to generalize the framework to the non-abelian cases
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