2018/03/13 by Marcel Bischoff, Bischoff, Marcel
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1803.04949
openalex publication_date 2018/03/13 · openalex created_date 2022/09/14 · openalex updated_date 2026/07/28
We show that all isomorphism classes of even rank Tambara-Yamagami categories\narise as \ℤ2-twisted representations of conformal nets. As a\nconsequence, we show that their Drinfel'd centers are realized by (generalized)\norbifolds of conformal nets associated with (self-dual) lattices. The quantum\ndouble subfactors of even rank Tambara-Yamagami categories are Bisch-Haagerup\nsubfactors and we describe their (dual) principal graphs.\n For every abelian group of odd order the Drinfel'd centers of the associated\nTambara-Yamagami categories give a fusion ring generalizing the Verlinde ring\n\Spin(2n+1)2 in the case of \ℤ2n+1. We classify all\ngeneralized metaplectic modular categories, i.e. unitary modular tensor\ncategory with those fusion rules and show that they are realized as\n\ℤ2-orbifolds of conformal nets associated with lattices. We further\nshow that twisted doubles of generalized dihedral groups of abelian groups of\nodd order are group-theoretical generalized metaplectic modular categories and\nvice versa.\n We give some examples of twisted orbifolds of conformal nets and show how\ngeneralized metaplectic modular categories arise by condensation of simpler\nones.\n