Papers › Computing the center of a fusion category
Computing the center of a fusion category
Fabian Mäurer, Ulrich Thiel
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We present an algorithm for explicitly computing the categorical (Drinfeld) center of a pivotal fusion category. Our approach is based on decomposing the images of simple objects under the induction functor from the category to its center. We have implemented this algorithm in a general-purpose software framework TensorCategories.jl for tensor categories that we develop within the open-source computer algebra system OSCAR. We compute explicit models for the centers in form of the tuples (X,γ) where X is an object and γ is a half-braiding. From these models we can compute the F-symbols and R-symbols. Using the data from the AnyonWiki, we were able to compute the center together with its F-symbols and R-symbols for all the 279 multiplicity-free fusion categories up to rank 5, and furthermore some chosen examples of rank 6, including the Haagerup subfactor (presented in a separate paper).
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