Vertex operator algebra with two Miyamoto involutions generating $S_3$

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In this article we study a VOA with two Miyamoto involutions generating $S_3$. In \cite{M3}, Miyamoto showed that a VOA generated by two conformal vectors whose Miyamoto involutions generate an automorphism group isomorphic to $S_3$ 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 $\mathrm{VA}(e,f)$ 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.
latex 26pages, new sections on simple current extensions and embedding into the moonshine VOA are added

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Quantum Algebra, 17B68, 17B69

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http://salesiana.dossiersoluciones.com/handle/123456789/64510

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0207117
 http://arxiv.org/abs/math/0207117

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arXiv