2024/06/19 by Fabian Mäurer, Mäurer, Fabian, Ulrich Thiel +1
Computer Science · #Category Theory (math.CT) #Computability, Logic, AI Algorithms #Constraint Satisfaction and Optimization #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Polynomial and algebraic computation #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2406.13438
openalex publication_date 2024/06/19 · openalex created_date 2024/06/22 · openalex updated_date 2026/08/01
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).