Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T21:11:35.754Z Has data issue: false hasContentIssue false
  • English
  • Français

A cyclotomic construction for Leech's lattice

Published online by Cambridge University Press:  26 February 2010

Maurice Craig
Maurice Craig
Affiliation:
Department of Mathematics, Western Illinois University, Macomb, Illinois 61455, U.S.A.
Get access

Extract

The 24 classes of even-valued, unimodular, positive quadratic forms in 24 variables have been determined by Niemeier [6]. One class is distinguished from the rest by the property that its forms have arithmetic minimum 4, rather than 2. The 24-dimensional lattice Λ corresponding to this form-class can therefore be identified with one found earlier by Leech [4], which has been studied extensively in connection with sporadic simple groups (e.g. [1]).

Type
Research Article
Information
Mathematika , Volume 25 , Issue 2 , December 1978 , pp. 236 - 241
Copyright
Copyright © University College London 1978

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Conway, J. H.. “A group of order 8, 315, 553, 613, 086, 720, 000”, Bull. London. Math. Soc., 1 (1969), 79–88.CrossRefGoogle Scholar
2.Conway, J. H.. “A characterization of Leech's lattice”, Invent. Math., 7 (1969), 137–142.CrossRefGoogle Scholar
3.Craig, M.. “Extreme forms and cyclotomy”, Mathematika, 25 (1978), 44–56.CrossRefGoogle Scholar
4.Leech, J.. “Some sphere packings in higher space”, Canad. J. Math., 16 (1964), 657–682.CrossRefGoogle Scholar
5.Leech, J.. “Notes on sphere packings”, Canad. J. Math., 19 (1967), 251–267.CrossRefGoogle Scholar
6.Niemeier, H.-V.. “Definite quadratische Formen der Dimension 24 und Diskriminante 1”, J. Number Theory, 5 (1973), 142–178.CrossRefGoogle Scholar