Well-rounded algebraic lattices in odd prime dimension
type: Item
instance of: scholarly article
title: Well-rounded algebraic lattices in odd prime dimension
zbMATH Open document ID: 1429.11118
author: Robson R. de Araujo
author: Sueli I. R. Costa
published in: Archiv der Mathematik
publication date: 2019-02-12T00:00:00Z
review text: A lattice is a discrete additive subgroup of ${\mathbb R}^d$. It is well-rounded if it has a subset of $d$ linearly independent vectors of minimum norm. The authors give a construction of well-rounded lattices in Euclidean space of odd prime dimension. They show that for each abelian number field of odd prime degree having square-free conductor, there exists a ${\mathbb Z}$-module $M$, where the canonical embedding applied to the module produces a well-rounded lattice. Additionally, they show that for each odd prime dimension there are infinitely many non-equivalent well-rounded algebraic lattices.
reviewed by: Steven T. Dougherty
Mathematics Subject Classification ID: 11H06
Mathematics Subject Classification ID: 11H71
zbMATH DE Number: 7021299
zbMATH Keywords: lattices
zbMATH Keywords: Minkowski embedding
zbMATH Keywords: well-rounded lattices
MaRDI profile type: Publication
full work available at URL: s00013-018-1232-7
OpenAlex ID: W2887480853
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DOI: 10.1007/S00013-018-1232-7
description: scientific article; zbMATH DE number 7021299