Z3-orbifold construction of the Moonshine vertex operator algebra and some maximal 3-local subgroups of the Monster

Hsian Yang Chen, Ching Hung Lam, Hiroki Shimakura

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this article, we describe some maximal 3-local subgroups of the Monster simple group using vertex operator algebras (VOA). We first study the holomorphic vertex operator algebra obtained by applying the orbifold construction to the Leech lattice vertex operator algebra and a lift of a fixed-point free isometry of order 3 of the Leech lattice. We also consider some of its special subVOAs and study their stabilizer subgroups using the symmetries of the subVOAs. It turns out that these stabilizer subgroups are 3-local subgroups of its full automorphism group. As one of our main results, we show that its full automorphism group is isomorphic to the Monster simple group by using a 3-local characterization and that the holomorphic VOA is isomorphic to the Moonshine VOA. This approach allows us to obtain relatively explicit descriptions of two maximal 3-local subgroups of the shape 3 1 + 12. 2. Suz : 2 and 3 8. Ω -(8 , 3). 2 in the Monster simple group.

Original languageEnglish
Pages (from-to)75-100
Number of pages26
JournalMathematische Zeitschrift
Volume288
Issue number1-2
DOIs
Publication statusPublished - 2018 Feb 1

Keywords

  • Primary 17B69
  • Secondary 20B25

ASJC Scopus subject areas

  • Mathematics(all)

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