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

@article{Lam2004VertexOA,
  title={Vertex operator algebras, extended \$E\_8\$ diagram, and McKay's observation on the Monster simple group},
  author={Ching Hung Lam and Hiromichi Yamada and Hiroshi Yamauchi},
  journal={Transactions of the American Mathematical Society},
  year={2004},
  volume={359},
  pages={4107-4123}
}
We 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 Eg diagram at each time. We then construct a certain coset (or commutant) subalgebra U associated with L in the lattice VOA V √2E8 . There are two natural conformal vectors of central charge 1/2… 
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References

SHOWING 1-10 OF 26 REFERENCES
Mckay's observation and vertex operator algebras generated by two conformal vectors of central charge 1/2
This paper is a continuation of (33) at which several coset subalgebras of the lattice VOA Vp 2E8 were constructed and the relationship between such algebras with the famous McKay observation on the
Binary Codes and Vertex Operator (Super)Algebras
Abstract We study a vertex operator algebra whose Virasoro element is a sum of pairwise orthogonal rational conformal vectors with central charge 1/2. The most important example is the moonshine
Decomposition of the lattice vertex operator algebra V2Al
Griess Algebras and Conformal Vectors in Vertex Operator Algebras
Abstract We define automorphisms of vertex operator algebra using the representations of the Virasoro algebra. In particular, we show that the existence of a special element, which we will call a
A new construction of the moonshine vertex operator algebra over the real number field
We give a new construction of the moonshine module vertex operator algebra V ? , which was originally constructed in [FLM2]. We construct it as a framed VOA over the real number field R. We also
Introduction to Vertex Operator Algebras and Their Representations
1 Introduction.- 1.1 Motivation.- 1.2 Example of a vertex operator.- 1.3 The notion of vertex operator algebra.- 1.4 Simplification of the definition.- 1.5 Representations and modules.- 1.6
Associative subalgebras of the Griess algebra and related topics
It is shown how certain idempotents in the Griess algebra generate the discrete series representations for the Virasoro algebra inside the Frenkel-Lepowsky-Meurman's moonshine module vertex operator
Sphere Packings, Lattices and Groups
The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to
Z4-Code Constructions for the Niemeier Lattices and their Embeddings in the Leech Lattice
TLDR
Z4-code constructions of the Niemeier lattices are given, showing their embedding in the Leech lattice, which yield an alternative proof of a recent result by Dong et al.
Algebra
THIS is a text–book intended primarily for undergraduates. It is designed to give a broad basis of knowledge comprising such theories and theorems in those parts of algebra which are mentioned in the
...
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