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Associative subalgebras of the Griess algebra and related topics
 Ohio State University
, 1996
"... In [DMZ] it was shown that the moonshine module V ♮ contains a sub vertex operator algebra isomorphic to the tensor product L ( 1 2, 0)⊗48 where L ( 1 ..."
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Cited by 24 (5 self)
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In [DMZ] it was shown that the moonshine module V ♮ contains a sub vertex operator algebra isomorphic to the tensor product L ( 1 2, 0)⊗48 where L ( 1
McKay’s observation and vertex operator algebras generated by two conformal vectors of central charge 1/2, in preparation
 MR 2006h:17034 Zbl 1082.17015 KENICHIRO TANABE AND HIROMICHI
"... This paper is a continuation of the authors ’ work [33] in which several coset subalgebras of the lattice VOA V √ were constructed and the relationship between such algebras ..."
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Cited by 6 (5 self)
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This paper is a continuation of the authors ’ work [33] in which several coset subalgebras of the lattice VOA V √ were constructed and the relationship between such algebras
VOAs generated by two conformal vectors whose τinvolutions generate S3
 J. Algebra
"... We determined the inner products of two conformal vectors with central charge 1 2 whose τinvolutions generates S3 if none of τinvolutions are trivial. We also see that a subVA generated by such conformal vectors is a VOA with central charge and has a Griess algebra of dimension three or four, resp ..."
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Cited by 2 (0 self)
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We determined the inner products of two conformal vectors with central charge 1 2 whose τinvolutions generates S3 if none of τinvolutions are trivial. We also see that a subVA generated by such conformal vectors is a VOA with central charge and has a Griess algebra of dimension three or four, respectively. 1 2
Octonions and the Leech lattice
, 2008
"... We give a new, elementary, description of the Leech lattice in terms of octonions, thereby providing the first real explanation of the fact that the number of minimal vectors, 196560, can be expressed in the form 3 × 240 × (1 + 16 + 16 × 16). We also give an easy proof that it is an even selfdual l ..."
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Cited by 2 (1 self)
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We give a new, elementary, description of the Leech lattice in terms of octonions, thereby providing the first real explanation of the fact that the number of minimal vectors, 196560, can be expressed in the form 3 × 240 × (1 + 16 + 16 × 16). We also give an easy proof that it is an even selfdual lattice. 1
The Classification of the Finite Simple Groups: An Overview
 MONOGRAFÍAS DE LA REAL ACADEMIA DE CIENCIAS DE ZARAGOZA. 26: 89–104, (2004)
, 2004
"... ..."
unknown title
, 2005
"... Ising vectors and automorphism groups of commutant subalgebras related to root systems ..."
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Ising vectors and automorphism groups of commutant subalgebras related to root systems
Hiroshi Yamauchi †
, 2006
"... On the structure of framed vertex operator algebras and their pointwise frame stabilizers ..."
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On the structure of framed vertex operator algebras and their pointwise frame stabilizers
Arithmetic groups and the affine E8 Dynkin diagram
, 2007
"... Several decades ago, John McKay suggested a correspondence between nodes of the affine E8 Dynkin diagram and certain conjugacy classes in the Monster group. Thanks to Monstrous Moonshine, this correspondence can be recast as an assignment of discrete subgroups of PSL2(R) to nodes of the affine E8 Dy ..."
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Several decades ago, John McKay suggested a correspondence between nodes of the affine E8 Dynkin diagram and certain conjugacy classes in the Monster group. Thanks to Monstrous Moonshine, this correspondence can be recast as an assignment of discrete subgroups of PSL2(R) to nodes of the affine E8 Dynkin diagram. The purpose of this article is to give an explanation for this latter correspondence using elementary properties of the group PSL2(R). We also obtain a super analogue of McKay’s observation, in which conjugacy classes of the Monster are replaced by conjugacy classes of Conway’s group — the automorphism group of the Leech lattice. 1
ISING VECTORS IN THE VERTEX OPERATOR ALGEBRA V + Λ ASSOCIATED WITH THE LEECH LATTICE Λ CHING HUNG LAM AND HIROKI SHIMAKURA
, 810
"... Abstract. In this article, we study the Ising vectors in the vertex operator algebra V + Λ associated with the Leech lattice Λ. The main result is a characterization of the Ising vectors in V + Λ. We show that for any Ising vector e in V Λ, there is a sublattice E ∼ = √ 2E8 of Λ such that e ∈ V + ..."
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Abstract. In this article, we study the Ising vectors in the vertex operator algebra V + Λ associated with the Leech lattice Λ. The main result is a characterization of the Ising vectors in V + Λ. We show that for any Ising vector e in V Λ, there is a sublattice E ∼ = √ 2E8 of Λ such that e ∈ V + E. Some properties about their corresponding τinvolutions in the moonshine vertex operator algebra V ♮ are also discussed. We show that there is no Ising vector of σtype in V ♮. Moreover, we compute the centralizer C Aut V ♮(z, τe) for any Ising vector e ∈ V + Λ, where z is a 2B element in Aut V ♮ which fixes V + Λ. Based on this result, we also obtain an explanation for the 1A case of an observation by GlaubermanNorton (2001), which describes some mysterious relations between the centralizer of z and some 2A elements commuting z in the Monster and the Weyl groups of certain sublattices of the root lattice of type E8. 1.
Vertex operators and sporadic groups
, 2007
"... In the 1980’s, the work of Frenkel, Lepowsky and Meurman, along with that of Borcherds, culminated in the notion of vertex operator algebra, and an example whose full symmetry group is the largest sporadic simple group: the Monster. Thus it was shown that the vertex operators of mathematical physics ..."
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In the 1980’s, the work of Frenkel, Lepowsky and Meurman, along with that of Borcherds, culminated in the notion of vertex operator algebra, and an example whose full symmetry group is the largest sporadic simple group: the Monster. Thus it was shown that the vertex operators of mathematical physics play a role in finite group theory. In this article we describe an extension of this phenomenon by introducing the notion of enhanced vertex operator algebra, and constructing examples that realize other sporadic simple groups, including one that is not involved in the Monster. 1