The Lattice O(5)
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 13:09:02 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
MINIMAL_NORM
DET
KISSING_NUMBER
GRAM
GROUP_ORDER
GROUP_GENERATORS
PROPERTIES
NOTES
REFERENCES
LAST_LINE
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NAME
O(5)
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DIMENSION
8
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MINIMAL_NORM
3
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DET
625
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KISSING_NUMBER
16
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GRAM
8 0
3
0 3
0 0 3
0 0 0 3
-1 1 1 1 3
1 -1 1 1 0 3
1 1 -1 1 0 0 3
1 1 1 -1 0 0 0 3
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GROUP_ORDER
384
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GROUP_GENERATORS
4
8 8
-1 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 0 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 -1
0 0 0 0 1 0 0 0
0 0 0 0 0 0 -1 0
8 8
0 0 0 0 0 1 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 -1
0 0 0 0 0 0 -1 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
8 8
1 0 0 0 0 0 0 0
0 0 -1 0 0 0 0 0
0 -1 0 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 -1
0 0 0 0 0 1 0 0
0 0 0 0 0 0 1 0
0 0 0 0 -1 0 0 0
8 8
1 0 0 0 0 0 0 0
0 0 0 -1 0 0 0 0
0 -1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 1
0 0 0 0 -1 0 0 0
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PROPERTIES
INTEGRAL=1
MODULAR=5
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NOTES
The "odd" version of Q_8(1).
Construction: Take vector v of norm 8 in L/2L, where L = Q_8(1) = H4.std
is the Icosian lattice; then this is nbr of Q_8(1) with respect to v.
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REFERENCES
E. M. Rains and N. J. A. Sloane,
The Shadow Theory of Modular and Unimodular Lattices,
J. Number Theory, 73 (1998), pp. 359-389;
http://neilsloane.com/doc/shad.pdf or shad.ps
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe