Tables of integral unimodular lattices constructed as \(k\)-neighbors in \(\mathbb{Z}^n\)
type: Item
instance of: scholarly article
title: Tables of integral unimodular lattices constructed as \(k\)-neighbors in \(\mathbb{Z}^n\)
zbMATH Open document ID: 0906.11033
author: Roland Bacher
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 1998-09-21T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/229556
full work available at URL: jtnb9-2.html
review text: Two lattices \(L\) and \(M\) on euclidean \({\mathbb R}^n\) are said to be \(k\)-neighbors for some positive integer \(k\) if both \(L/(L\cap M)\) and \(M/(L\cap M)\) are cyclic groups of order \(k\). The integral \(k\)-neighbors of the standard lattice \({\mathbb Z}^n\) represent all classes of self-dual lattices (the proof is sketched). In the tables published here one can find such a description for any class up to \(n=24\), together with some information related to the enumeration of these lattices in [\textit{J. H. Conway} and \textit{N. J. A. Sloane}, Sphere packings, lattices and groups. 2nd ed. (1993; Zbl 0785.11036)].
Mathematics Subject Classification ID: 11H06
Mathematics Subject Classification ID: 11E12
Mathematics Subject Classification ID: 11-04
zbMATH DE Number: 1164099
zbMATH Keywords: unimodular lattice
zbMATH Keywords: neighbor lattice
reviewed by: Heinz-Georg Quebbemann
MaRDI profile type: Publication
OpenAlex ID: W2464511352
cites work: Q4039784
cites work: Klassenzahlen definiter quadratischer Formen
cites work: Q3973942
cites work: Q4237381
DOI: 10.5802/JTNB.214
description: scientific article; zbMATH DE number 1164099