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A construction of integral lattices
Author(s) -
Quebbemann H.-G.
Publication year - 1984
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300010731
Subject(s) - mathematics , lattice (music) , quotient , discriminant , pure mathematics , simple (philosophy) , dimension (graph theory) , combinatorics , philosophy , physics , epistemology , artificial intelligence , computer science , acoustics
Given an integral lattice L and a hyperbolic decomposition of some quotient L/pL , there is a simple technique for obtaining other lattices of the same dimension and discriminant as L ⊥ … ⊥ L . When applied to the D 4 and E 8 root lattices, for example, this yields a new sphere packing in ℝ 32 , which is denser than those known up to now, and an extremal type II lattice in ℝ 64 .