Reconstructing Braided Subcategories of SU(N)_k

2022/01/31 by Feng, Zhaobidan, Rowell, Eric C., Ming, Shuang
#Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2202.00121

Abstract

Ocneanu rigidity implies that there are finitely many (braided) fusion categories with a given set of fusion rules. While there is no method for determining all such categories up to equivalence, there are a few cases for which can. For example, Kazhdan and Wenzl described all fusion categories with fusion rules isomorphic to those of SU(N)_k. In this paper we extend their results to a statement about braided fusion categories, and obtain similar results for certain subcategories of SU(N)_k.

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