Vertex operator algebra with two Miyamoto involutions generating S₃

2002/07/13 by Shinya Sakuma, Sakuma, Shinya, Hiroshi Yamauchi +1
Mathematics · Physics and Astronomy · #17B68 #17B69 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA #msc:17B68 #msc:17B69

paper · pdf · doi:10.48550/arxiv.math/0207117

latex 26pages, new sections on simple current extensions and embedding into the moonshine VOA are added

openalex publication_date 2002/07/13 · arxiv created 2002/09/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we study a VOA with two Miyamoto involutions generating S₃. In \citeM3, Miyamoto showed that a VOA generated by two conformal vectors whose Miyamoto involutions generate an automorphism group isomorphic to S₃ is isomorphic to one of the four candidates he listed. We construct one of them and prove that our VOA is actually the same as VA(e,f) studied by Miyamoto. We also show that there is an embedding into the moonshine VOA. Using our VOA, we can define the 3A-triality in the Monster.

Citations

• Symmetric invariant bilinear forms on vertex operator algebras

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• McKay's observation and vertex operator algebras generated by two conformal vectors of central charge 1/2
• A new construction of the moonshine vertex operator algebra over the real number field
• A new existence proof of the Monster by VOA theory
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