McKay's observation and vertex operator algebras generated by two conformal vectors of central charge 1/2

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dc.creatorLam, Ching Hung
dc.creatorYamada, Hiromichi
dc.creatorYamauchi, Hiroshi
dc.date2005-03-13
dc.date.accessioned2026-07-07T05:17:54Z
dc.date.available2026-07-07T05:17:54Z
dc.descriptionThis paper is a continuation of our paper math.QA/0403010 at which several coset subalgebras of the lattice VOA $V_{\sqrt{2}E_8}$ were constructed and the relationship between such algebras with the famous McKay observation on the extended E_8 diagram and the Monster simple group were discussed. In this article, we shall provide the technical details. We completely determine the structure of the coset subalgebras constructed and show that they are all generated by two conformal vectors of central charge 1/2. We also study the representation theory of these coset subalgebras and show that the product of two Miyamoto involutions is in the desired conjugacy class of the Monster simple group if a coset subalgebra U is actually contained in the Moonshine VOA. The existence of U inside the Moonshine VOA for the cases of 1A, 2A, 2B and 4A is also established. Moreover, the cases for 3A, 5A and 3C are discussed.
dc.description52 pages, no figure
dc.identifierhttps://arxiv.org/abs/math/0503239
dc.identifierhttp://arxiv.org/abs/math/0503239
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74472
dc.subjectQuantum Algebra
dc.subjectGroup Theory
dc.subject17B68; 17B69; 20D08
dc.titleMcKay's observation and vertex operator algebras generated by two conformal vectors of central charge 1/2
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