2018/03/13 by Marcel Bischoff, Bischoff, Marcel
Mathematics · Physics and Astronomy · #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) #math-ph #math.CT #math.MP #math.OA #math.QA
paper · pdf · doi:10.48550/arxiv.1803.04949
36 pages, comments are welcome!
arxiv created 2018/03/13 · openalex publication_date 2018/03/13 · arxiv updated 2018/03/14 · openalex created_date 2022/09/14 · openalex updated_date 2026/07/28
We show that all isomorphism classes of even rank Tambara-Yamagami categories arise as ℤ2-twisted representations of conformal nets. As a consequence, we show that their Drinfel'd centers are realized by (generalized) orbifolds of conformal nets associated with (self-dual) lattices. The quantum double subfactors of even rank Tambara-Yamagami categories are Bisch-Haagerup subfactors and we describe their (dual) principal graphs. For every abelian group of odd order the Drinfel'd centers of the associated Tambara-Yamagami categories give a fusion ring generalizing the Verlinde ring Spin(2n+1)2 in the case of ℤ2n+1. We classify all generalized metaplectic modular categories, i.e. unitary modular tensor category with those fusion rules and show that they are realized as ℤ2-orbifolds of conformal nets associated with lattices. We further show that twisted doubles of generalized dihedral groups of abelian groups of odd order are group-theoretical generalized metaplectic modular categories and vice versa. We give some examples of twisted orbifolds of conformal nets and show how generalized metaplectic modular categories arise by condensation of simpler ones.