Vertex operator algebra with two Miyamoto involutions generating S3

Abstract In this article we study a VOA with two Miyamoto involutions generating S 3 . In [ math.GR/0112031 ], 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 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 of the Monster.