On rationality of vertex operator superalgebras

2013/02/26 by Chongying Dong, Dong, Chongying, Jianzhi Han +1
Mathematics · Physics and Astronomy · #17B69 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1302.6360

openalex publication_date 2013/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is proved that g-rationality of a vertex operator superalgebra V=V₀+V₁ for all g in G imply rationality of V^G, and also imply that each irreducible V^G-module is a submodule of an irreducible g-twisted V-module for some g in G, where G is any finite abelian subgroup of Aut(V). We also prove that for any finite solvable G, rationality of V^G implies g-rationality of V for any g in G.

Citations

• Local systems of vertex operators, vertex superalgebras and modules
• Representation theory and tensor product theory for vertex operator algebras
• Quantum Dimensions and Quantum Galois Theory

Related

• Twisted representations of vertex operator superalgebras
• Rationality of vertex operator algebras
• Bimodules and g-rationality of vertex operator algebras
• Some finite properties for vertex operator superalgebras
• Rationality of holomorphic vertex operator algebras