Prime decomposition of modular tensor categories of local modules of\n Type D

2018/10/21 by Andrew Schopieray, Schopieray, Andrew
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1810.09057

openalex publication_date 2018/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \C( mathfrakg,k) be the unitary modular tensor categories\narising from the representation theory of quantum groups at roots of unity for\narbitrary simple finite-dimensional complex Lie algebra mathfrakg and\npositive integer levels k. Here we classify nondegenerate fusion\nsubcategories of the modular tensor categories of local modules\n\C( mathfrakg,k)_R⁰ where R is the regular algebra of Tannakian\n\Rep(H)\⊂\C( mathfrakg,k)_\pt. For\n mathfrakg= mathfrakso₅ we describe the decomposition of\n\C( mathfrakg,k)_R⁰ into prime factors explicitly and as an\napplication we classify relations in the Witt group of nondegenerately braided\nfusion categories generated by the equivalency classes of\n\C( mathfrakso₅,k) and \C( mathfrakg₂,k) for\nk\∈\ℤ_\≥1.\n

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