The Lattice D4 as a Hurwitzian lattice

An entry from the Catalogue of Lattices, which is a joint project of
Neil J. A. Sloane, AT&T Labs-Research (njas@research.att.com) and
Gabriele Nebe, University of Ulm (nebe@mathematik.uni-ulm.de)

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DIVISORS
GRAM
MINIMAL_NORM
KISSING_NUMBER
HERMITIAN_GROUP_ORDER
HERMITIAN_GROUP_GENERATORS
HERMITIAN_STRUCTURE
PROPERTIES
REFERENCES
NOTES
LAST_LINE

• NAME
  D4 as a Hurwitzian lattice
  
• DIMENSION
  4
  
• DIVISORS
  2^2
  
• GRAM
  4 0
  2
  0 2
  0 0 2
  1 1 1 2
  
• MINIMAL_NORM
  2
  
• KISSING_NUMBER
  24
  
• HERMITIAN_GROUP_ORDER
  2^3 * 3
  
• HERMITIAN_GROUP_GENERATORS
  2
  4 4
  0 0 1 0
  1 1 1 -2
  -1 0 0 0
  0 1 1 -1
  4 4
  0 0 0 1
  0 1 1 -1
  -1 -1 0 1
  -1 0 0 1
  
• HERMITIAN_STRUCTURE
  4
  4 4
  1 0 0 0
  0 1 0 0
  0 0 1 0
  0 0 0 1
  4 4
  0 -1 0 0
  1 0 0 0
  -1 -1 -1 2
  0 -1 -1 1
  4 4
  1 1 1 -2
  0 0 1 0
  0 -1 0 0
  1 0 1 -1
  4 4
  0 0 0 -1
  1 0 1 -1
  0 -1 -1 1
  1 0 0 -1
  
• PROPERTIES
  Modular=1
  HermitianUnimodular = 1
  
• REFERENCES
  C. Bachoc, Voisinage au sens de Kneser pour les r\'eseaux quaternioniens.
  Comment. Math. Helvetici 70 (1995), 350-374.
  
  Bachoc, Nebe: Classification of two genera of 32-dimensional lattices
  over the Hurwitz order
  
• NOTES
  Normform of the Hurwitz order, D4=F4
  
• LAST_LINE
  
  

INDEX FILE | ABBREVIATIONS

[ AT&T Labs Research | Our People | Our Work | History | Find ]