Mathematical Foundation of Topological Order
We know that group theory is the mathematical foundation of symmetry breaking orders. What is the mathematical foundation of topological order? The string-net condensation suggests that tensor category (or monoidal category) theory may be the mathematical foundation of topological order. Quantum operator algebra is a very important mathematical tool in studying topological orders. A subclass of toplogical order—Abelian topological order in two dimensions—can be classified by a K-matrix approach. Some also suggest that topological order is mathematically described by extended quantum symmetry.
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