Английская Википедия:Barnes–Wall lattice
In mathematics, the Barnes–Wall lattice Λ16, discovered by Eric Stephen Barnes and G. E. (Tim) Wall (Шаблон:Harvtxt), is the 16-dimensional positive-definite even integral lattice of discriminant 28 with no norm-2 vectors. It is the sublattice of the Leech lattice fixed by a certain automorphism of order 2, and is analogous to the Coxeter–Todd lattice.
The automorphism group of the Barnes–Wall lattice has order 89181388800 = 221 35 52 7 and has structure 21+8 PSO8+(F2). There are 4320 vectors of norm 4 in the Barnes–Wall lattice (the shortest nonzero vectors in this lattice).
The genus of the Barnes–Wall lattice was described by Шаблон:Harvtxt and contains 24 lattices; all the elements other than the Barnes–Wall lattice have root system of maximal rank 16.
The Barnes–Wall lattice is described in detail in Шаблон:Harv.
References
External links
- Barnes–Wall lattice at Sloane's lattice catalogue.