The Lattice E8 (as a Hurwitzian lattice)
An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, RWTH Aachen University
(nebe@math.rwth-aachen.de)
and
Neil J. A. Sloane
(njasloane@gmail.com)
Last modified Fri Jul 18 13:15:59 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
GRAM
MINIMAL_NORM
KISSING_NUMBER
HERMITIAN_GROUP_NAME
HERMITIAN_GROUP_ORDER
HERMITIAN_GROUP_GENERATORS
HERMITIAN_STRUCTURE
PROPERTIES
REFERENCES
NOTES
LAST_LINE
-
NAME
E8 (as a Hurwitzian lattice)
-
DIMENSION
8
-
DET
1
-
GRAM
8 8
2 -1 -1 -1 -1 1 -1 1
-1 2 0 1 0 -1 1 0
-1 0 2 1 1 0 1 0
-1 1 1 2 1 -1 1 0
-1 0 1 1 2 -1 1 -1
1 -1 0 -1 -1 2 -1 1
-1 1 1 1 1 -1 2 0
1 0 0 0 -1 1 0 2
-
MINIMAL_NORM
2
-
KISSING_NUMBER
240
-
HERMITIAN_GROUP_NAME
2^1+4_-.Alt_5
-
HERMITIAN_GROUP_ORDER
2^7 * 3 * 5
-
HERMITIAN_GROUP_GENERATORS
2
8 8
0 0 0 0 0 0 0 1
0 0 0 0 -1 0 0 -1
0 0 0 0 0 1 1 -1
0 0 0 0 -1 0 1 -1
0 1 0 -1 1 0 0 0
0 0 0 1 0 1 0 0
-1 0 0 -1 0 0 0 0
0 0 1 0 -1 0 0 0
8 8
-1 -2 -1 1 -1 0 1 0
0 1 0 -1 0 0 0 0
1 1 0 1 0 1 0 -1
0 1 0 0 0 0 0 0
0 1 0 0 1 0 -1 1
0 -1 0 1 -1 0 0 -1
0 1 -1 0 1 1 0 0
-1 -1 -1 1 -1 1 1 -1
-
HERMITIAN_STRUCTURE
4
4
8 8
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 1
8 8
0 0 1 -1 1 -1 -1 1
1 0 0 0 -1 0 1 -1
0 1 0 0 0 1 0 -1
1 1 1 0 -1 0 0 -1
0 0 0 1 -1 0 0 -1
0 1 0 -1 2 0 -1 1
1 0 0 1 -1 1 1 -2
1 1 1 -1 1 0 0 0
8 8
-1 -1 -1 0 0 -1 0 1
1 0 1 1 -1 0 0 -1
1 1 1 -1 1 0 -1 0
0 0 1 0 0 0 -1 0
0 1 0 0 1 1 -1 0
0 0 0 -1 0 -1 0 1
1 1 1 0 1 0 -1 0
0 0 1 -1 0 -2 -1 1
8 8
-1 0 0 -1 1 -1 -1 1
1 -1 0 1 -1 0 1 -1
1 1 0 0 0 1 0 -1
1 0 1 0 -1 0 0 -1
0 0 0 1 -1 1 0 -1
0 1 0 -1 1 -1 -1 1
1 0 0 1 0 1 0 -1
1 1 1 -1 1 -1 -1 0
-
PROPERTIES
Unimodular=1
-
REFERENCES
Bachoc, Nebe: Classification of two genera of 32-dimensional lattices
over the Hurwitz order
-
NOTES
This is the unique structure of E8 over the Hurwitz order
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe