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

✍ Scribed by Masahiko Miyamoto

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 245 KB
Volume: 268
Category: Article
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(03)00096-6

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✦ Synopsis

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 conformal vectors e and f and showed a subVA generated by e and f is a VOA with central charge 1/2 + 20/21 or 4/5 + 6/7 and has a Griess algebra of dimension three or four, respectively.

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Vertex operator algebra with two Miyamoto involutions generating S3

✍ Shinya Sakuma; Hiroshi Yamauchi 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 245 KB

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 con