On quantum Galois theory

1994/12/05 by Chongying Dong, Dong, Chongying, Geoffrey Mason +1 · 5 citations
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.hep-th/9412037

openalex publication_date 1994/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a simple vertex operator algebra V and a finite automorphism group G of V then V is a direct sum of V^χ where χ are irreducible character of G and V^χ is the subspace of V which G acts according to the character χ. We prove the following: 1. Each V^χ is nonzero. 2. V^χ is a tensor product M_χ⊗ V_χ where M_χ is an irreducible G-module affording χ and V_χ is a V^G-module. If G is solvable, V_χ is a simple V^G-module and M_χ↦ V_χ is a bijection from the set of irreducible G-modules to the set of (inequivalent) simple V^G-modules which are contained in V.

Cited by

• Structure and representations of the coset vertex operator algebra C( L_\widehatosp(1|2)(2,0), L_\widehatosp(1|2)(1,0)^{⊗ 2})
• Y(z)-injective vertex superalgebras and Hopf actions
• A tensor category construction of the W_p,q triplet vertex operator algebra and applications
• Generalized Symmetries From Fusion Actions
• On the operator content of nilpotent orbifold models

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