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Classification of eight-dimensional perfect forms


Authors: Mathieu Dutour Sikiric, Achill Schürmann and Frank Vallentin
Journal: Electron. Res. Announc. Amer. Math. Soc. 13 (2007), 21-32
MSC (2000): Primary 11H31, 11H55; Secondary 52B55
Published electronically: April 11, 2007
MathSciNet review: 2300003
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Abstract: In this paper, we classify the perfect lattices in dimension $ 8$. There are $ 10916$ of them. Our classification heavily relies on exploiting symmetry in polyhedral computations. Here we describe algorithms making the classification possible.


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Additional Information

Mathieu Dutour Sikiric
Affiliation: Institut Rudjer Bosković, Zagreb, Croatia
Email: Mathieu.Dutour@ens.fr

Achill Schürmann
Affiliation: Otto-von-Guericke-University, Magdeburg, Germany
Email: Achill.Schuermann@Mathematik.Uni-Magdeburg.de

Frank Vallentin
Affiliation: CWI, Amsterdam, The Netherlands
Email: f.vallentin@cwi.nl

DOI: http://dx.doi.org/10.1090/S1079-6762-07-00171-0
Received by editor(s): September 15, 2006
Published electronically: April 11, 2007
Additional Notes: The second and the third author were supported by the Deutsche Forschungsgemeinschaft (DFG) under grant SCHU 1503/4-1. During the work on this paper the third author was also partially supported by the Edmund Landau Center for Research in Mathematical Analysis and Related Areas, sponsored by the Minerva Foundation (Germany), and he was partially supported by the Netherlands Organization for Scientific Research under grant NWO 639.032.203.
Communicated by: Robert Griess
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.