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Perfect lattices in euclidean spaces / Jacques MARTINET (Cop. 2003)
Titre : Perfect lattices in euclidean spaces Type de document : texte imprimé Auteurs : Jacques MARTINET, Auteur Editeur : Berlin : Springer-Verlag Année de publication : Cop. 2003 Collection : Grundlehren der mathematischen wissenschaften, ISSN 0072-7830 num. 327 Importance : XVIII-523 p. ISBN/ISSN/EAN : 978-3-540-44236-3 Langues : Anglais Catégories : 11H31
11H55
11H56
11H71Mots-clés : treillis espace euclidien Résumé : Lattices are discrete subgroups of maximal rank in a Euclidean space. To each such geometrical object, we can attach a canonical sphere packing which, assuming some regularity, has a density. The question of estimating the highest possible density of a sphere packing in a given dimension is a fascinating and difficult problem: the answer is known only up to dimension 3.
This book thus discusses a beautiful and central problem in mathematics, which involves geometry, number theory, coding theory and group theory, centering on the study of extreme lattices, i.e. those on which the density attains a local maximum, and on the so-called perfection property.
Written by a leader in the field, it is closely related to, though disjoint in content from, the classic book by J.H. Conway and N.J.A. Sloane, Sphere Packings, Lattices and Groups, published in the same series as vol. 290.
Every chapter except the first and the last contains numerous exercises. For simplicity those chapters involving heavy computational methods contain only few exercises. It includes appendices on Semi-Simple Algebras and Quaternions and Strongly Perfect Lattices.Note de contenu : index, références Perfect lattices in euclidean spaces [texte imprimé] / Jacques MARTINET, Auteur . - Berlin : Springer-Verlag, Cop. 2003 . - XVIII-523 p.. - (Grundlehren der mathematischen wissenschaften, ISSN 0072-7830; 327) .
ISBN : 978-3-540-44236-3
Langues : Anglais
Catégories : 11H31
11H55
11H56
11H71Mots-clés : treillis espace euclidien Résumé : Lattices are discrete subgroups of maximal rank in a Euclidean space. To each such geometrical object, we can attach a canonical sphere packing which, assuming some regularity, has a density. The question of estimating the highest possible density of a sphere packing in a given dimension is a fascinating and difficult problem: the answer is known only up to dimension 3.
This book thus discusses a beautiful and central problem in mathematics, which involves geometry, number theory, coding theory and group theory, centering on the study of extreme lattices, i.e. those on which the density attains a local maximum, and on the so-called perfection property.
Written by a leader in the field, it is closely related to, though disjoint in content from, the classic book by J.H. Conway and N.J.A. Sloane, Sphere Packings, Lattices and Groups, published in the same series as vol. 290.
Every chapter except the first and the last contains numerous exercises. For simplicity those chapters involving heavy computational methods contain only few exercises. It includes appendices on Semi-Simple Algebras and Quaternions and Strongly Perfect Lattices.Note de contenu : index, références Exemplaires
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