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Vertex operator algebra with two Miyamoto involutions generating S3

✍ Scribed by Shinya Sakuma; Hiroshi Yamauchi

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 245 KB
Volume: 267
Category: Article
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(03)00170-4

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✦ Synopsis

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.

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Vertex operator algebras generated by two conformal vectors whose τ-involutions generate S3

✍ Masahiko Miyamoto 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 245 KB

We study a vertex operator algebra (VOA) V of moonshine type with two τ -involutions φ and ψ which generate S 3 . In this case, V contains rational conformal vectors e and f with central charge 1/2 such that φ = τ e , ψ = τ f , and e τ f τ e = f . We determined the inner products e, f for such confo