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

DOI10.1090/S0002-9947-07-04002-0zbMath1139.17011arXivmath/0403010OpenAlexW2093685375MaRDI QIDQ3443124

Ching Hung Lam, Hiroshi Yamauchi, Hiromichi Yamada

Publication date: 31 May 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0403010

zbMATH Keywords

vertex operator algebrasMonster simple groupconformal vectorsMcKay's observationcoset subalgebras

Mathematics Subject Classification ID

Simple groups: sporadic groups (20D08) Virasoro and related algebras (17B68) Vertex operators; vertex operator algebras and related structures (17B69)

Related Items (16)

The Conway-Miyamoto correspondences for the Fischer 3-transposition groups ⋮ Sigma involutions associated with parafermion vertex operator algebra K(sl2,k) ⋮ Ising vectors and automorphism groups of commutant subalgebras related to root systems ⋮ \(\mathbb{Z}_{2k}\)-code vertex operator algebras ⋮ Vertex operator algebras generated by two Ising vectors ⋮ The VOAs generated by two Ising vectors \(e\) and \(f\) with \(\langle e, f \rangle = \frac{1}{2^8}, |\tau_e \tau_f| = 3\) or \(\langle e, f \rangle = \frac{3}{2^9}\) ⋮ Uniqueness of VOA structure of \(3C\)-algebra and \(5A\)-algebra ⋮ Module categories of simple current extensions of vertex operator algebras. ⋮ On \(\mathbb {Z}_p\)-orbifold constructions of the Moonshine vertex operator algebra ⋮ On the structure of framed vertex operator algebras and their pointwise frame stabilizers ⋮ \(6A\)-algebra and its representations ⋮ 2A-orbifold construction and the baby-monster vertex operator superalgebra ⋮ Vertex operator algebras associated to the Virasoro algebra over an arbitrary field ⋮ McKay's \(E_6\) observation on the largest Fischer group ⋮ Griess algebras generated by the Griess algebras of two \(3A\)-algebras with a common axis ⋮ Weyl groups and vertex operator algebras generated by Ising vectors satisfying the (2B, 3C) condition

Cites Work

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• A simple construction for the Fischer-Griess monster group
• The friendly giant
• An \(E_ 8-\)approach to the Leech lattice and the Conway group
• Vertex algebras associated with even lattices
• Introduction to vertex operator algebras and their representations
• Decomposition of the lattice vertex operator algebra \(V_{\sqrt{2}A_l}\).
• \(\mathbb{Z}_4\)-code constructions for the Niemeier lattices and their embeddings in the Leech lattice
• A new construction of the moonshine vertex operator algebra over the real number field
• Griess algebras and conformal vectors in vertex operator algebras
• Binary codes and vertex operator (super)algebras
• On axiomatic approaches to vertex operator algebras and modules

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