Lattices like the Leech lattice

DOI10.1016/0021-8693(90)90110-AzbMath0701.11021MaRDI QIDQ913845

Richard E. Borcherds

Publication date: 1990

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

zbMATH Keywords

Barnes-Wall latticeLeech latticegroup of automorphismsreflection groupLorentzian latticeCoxeter-Todd lattice

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Lattices and convex bodies (number-theoretic aspects) (11H06) Reflection groups, reflection geometries (51F15) Automorphism groups of lattices (11H56)

Related Items (12)

Natural construction of ten Borcherds-Kac-Moody algebras associated with elements in \(M_{23}\) ⋮ The 290 fixed-point sublattices of the Leech lattice ⋮ Fun with \(F_{24}\) ⋮ Automorphic forms, fake monster algebras, and hyperbolic reflection groups ⋮ Monstrous moonshine and monstrous Lie superalgebras ⋮ Arithmetic hyperbolic reflection groups ⋮ Covering aspects of the Niemeier lattices ⋮ New complex- and quaternion-hyperbolic reflection groups ⋮ Reflection groups of Lorentzian lattices ⋮ A new complex reflection group in \(PU(9,1)\) and the Barnes-Wall lattice ⋮ Classification of positive definite lattices ⋮ The monster Lie algebra

Cites Work

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• Automorphism groups of Lorentzian lattices
• Generalized Kac-Moody algebras
• The automorphism group of the 26-dimensional even unimodular Lorentzian lattice
• The Leech lattice
• Monstrous Moonshine

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