2021/08/11 by Chongying Dong, Dong, Chongying, Siu‐Hung Ng +3 · 2 citations
Mathematics · Physics and Astronomy · #17B69 #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2108.05225
openalex publication_date 2021/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let V be a simple, rational, C2-cofinite vertex operator algebra and G a finite group acting faithfully on V as automorphisms, which is simply called a rational vertex operator algebra with a G-action. It is shown that the category \cal EVG generated by the VG-submodules of V is a symmetric fusion category braided equivalent to the G-module category \cal E=\rm Rep(G). If V is holomorphic, then the VG-module category \cal CVG is a minimal modular extension of \cal E, and is equivalent to the Drinfeld center \cal Z(\rm VecGα) as modular tensor categories for some α∈ H3(G,S1) with a canonical embedding of \cal E. Moreover, the collection \cal Mv(\cal E) of equivalence classes of the minimal modular extensions \cal CVG of \cal E for holomorphic vertex operator algebras V with a G-action form a group, which is isomorphic to a subgroup of H3(G,S1). Furthermore, any pointed modular category \cal Z(\rm VecGα) is equivalent to \cal CVLG for some positive definite even unimodular lattice L. In general, for any rational vertex operator algebra U with a G-action, \cal CUG is a minimal modular extension of the braided fusion subcategory \cal F generated by the UG-submodules of U-modules. Furthermore, the group \cal Mv(\cal E) acts freely on the set of equivalence classes \cal Mv(\cal F) of the minimal modular extensions \cal CWG of \cal F for any rational vertex operators algebra W with a G-action.