An E8-approach to the moonshine vertex operator algebra

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Abstract

In this article, we study the moonshine vertex operator algebra starting with the tensor product of three copies of the vertex operator algebra V √2E8+, and describe it by the quadratic space over double-struck F sign2 associated to V√2E8 +. Using quadratic spaces and orthogonal groups, we show the transitivity of the automorphism group of the moonshine vertex operator algebra on the set of all full vertex operator subalgebras isomorphic to the tensor product of three copies of V√2E8+, and determine the stabilizer of such a vertex operator subalgebra. Our approach is a vertex operator algebra analogue of 'An E8-approach to the Leech lattice and the Conway group' by Lepowsky and Meurman. Moreover, we find new analogies among the moonshine vertex operator algebra, the Leech lattice and the extended binary Golay code.

Original languageEnglish
Pages (from-to)493-516
Number of pages24
JournalJournal of the London Mathematical Society
Volume83
Issue number2
DOIs
Publication statusPublished - 2011 Apr
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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