Decomposition of the Moonshine Vertex Operator Algebra as Virasoro Modules

✍ Scribed by Masaaki Kitazume; Ching Hung Lam; Hiromichi Yamada

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 185 KB
• Volume: 226
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1999.8206

✦ Synopsis

In this article, we obtain a decomposition of the Moonshine vertex operator h Ž Ž . Ž . Ž .. m12 algebra V associated with the algebra L 1r2, 0 m L 7r10, 0 m L 4r5, 0 . Our method is based on a coset decomposition of the Leech lattice ⌳ associated 12 ' Ž . with 2 A using some codes. In fact, we construct a code vertex operator 2 algebra M k m M t with a ternary code D D and a ‫ޚ‬ = ‫ޚ‬ code C C and use it to C C D D 2 2 obtain a decomposition of V h . ᮊ 2000 Academic Press 1. INTRODUCTION Ž . Vertex operator algebras VOAs as modules of a tensor product of rational Virasoro vertex operator algebras were first studied by Dong et al. w x h 7 . They showed that the Moonshine VOA V contains 48 mutually 1 orthogonal elements, called conformal vectors of central charge , such 2 that each of them will generate a copy of the rational Virasoro VOA 1 h Ž . L , 0 inside V and the sum of these 48 conformal vectors is the 2 Virasoro element of V h . In other words, the Moonshine VOA contains a 893