Anyons in two-dimensional topological order are expected to be useful for topological quantum computations and their behaviors are described with modular tensor categories mathematically. We have a method to deal with them using 4-tensors and matrix product operators, and then we need only finite dimensional Hilbert spaces and operators. Mathematical structures appearing here are the same as what have been studied in theory of operator algebras for nearly 30 years. I will present basics of this theory in an elementary way without assuming any prior knowledge on operator algebras.
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