Vertex operator algebras, extended E_8 diagram, and McKay's observation on the Monster simple group

Simple item page
dc.creatorLam, Ching Hung
dc.creatorYamada, Hiromichi
dc.creatorYamauchi, Hiroshi
dc.date2004-02-29
dc.date.accessioned2026-07-07T05:05:48Z
dc.date.available2026-07-07T05:05:48Z
dc.descriptionWe study McKay's observation on the Monster simple group, which relates the 2A-involutions of the Monster simple group to the extended E_8 diagram, using the theory of vertex operator algebras (VOAs). We first consider the sublattices L of the E_8 lattice obtained by removing one node from the extended E_8 diagram at each time. We then construct a certain coset (or commutant) subalgebra U associated with L in the lattice VOA V_{\sqrt{2}E_8}. There are two natural conformal vectors of central charge 1/2 in U such that their inner product is exactly the value predicted by Conway. The Griess algebra of U coincides with the algebra described in Conway's paper. There is a canonical automorphism of U of order |E_8/L|. Such an automorphism can be extended to the Leech lattice VOA V_Λand it is in fact a product of two Miyamoto involutions. In the sequel [LYY] to this article we shall develop the representation theory of $U$. It is expected that if U is actually contained in the Moonshine VOA V^\natural, the product of two Miyamoto involutions is in the desired conjugacy class of the Monster simple group.
dc.identifierhttps://arxiv.org/abs/math/0403010
dc.identifierhttp://arxiv.org/abs/math/0403010
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70307
dc.subjectQuantum Algebra
dc.subjectGroup Theory
dc.subject17B68, 17B69, 20D08
dc.titleVertex operator algebras, extended E_8 diagram, and McKay's observation on the Monster simple group
dc.typetext

Files

Collections

arXiv