Vertex operator algebra with two Miyamoto involutions generating $S_3$

Details Vertex operator algebra with two Miyamoto involutions generating $S_3$ Vertex operator algebra with two Miyamoto involutions generating $S_3$

2002-07-13

arxiv.org/abs/math/0207117v3

Mathematics

Quantum Algebra

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

Scientific paper

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.

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