An \(E_ 8-\)approach to the Leech lattice and the Conway group

DOI10.1016/0021-8693(82)90268-XzbMath0501.20014MaRDI QIDQ1172146

James Lepowsky, Arne Meurman

Publication date: 1982

Published in: Journal of Algebra (Search for Journal in Brave)

zbMATH Keywords

Weyl groupautomorphism groupLeech latticesporadic simple grouproot latticemaximal 2-local subgroupFriendly Giant

Mathematics Subject Classification ID

Simple groups: sporadic groups (20D08) Automorphisms of abstract finite groups (20D45) Finite simple groups and their classification (20D05)

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A sublattice of the Leech lattice ⋮ Vertex operator algebras, extended $E_8$ diagram, and McKay's observation on the Monster simple group ⋮ A lattice theoretical construction of a GAB of the Suzuki sporadic simple group ⋮ Self-dual lattices of type \(A\) ⋮ Pieces of eight: semiselfdual lattices and a new foundation for the theory of Conway and Mathieu groups ⋮ On extremal even unimodular 72-dimensional lattices ⋮ Finite groups ⋮ Midwest cousins of Barnes-Wall lattices ⋮ Rank 72 high minimum norm lattices ⋮ Elliptic genera and the moonshine module ⋮ Physical vacuum properties and internal space dimension ⋮ Moonshine vertex operator algebra as \(L(\frac{1}{2},0)\otimes L(\frac{7}{10},0) \otimes L(\frac{4}{5},0) \otimes L(1,0)\)-modules

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