Algebraic construction of lattices via maximal quaternion orders

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dc.contributor.authorBenedito, Cintya Wink de Oliveira [UNESP]
dc.contributor.authorAlves, Carina [UNESP]
dc.contributor.authorBrasil Jr, Nelson Gomes
dc.contributor.authorCosta, Sueli Irene Rodrigues
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionUniversidade Estadual de Campinas (UNICAMP)
dc.date.accessioned2020-12-12T00:54:56Z
dc.date.available2020-12-12T00:54:56Z
dc.date.issued2020-05-01
dc.description.abstractIn this paper we propose a framework to construct algebraic lattices in dimensions 4n via ideals from maximal orders of a quaternion algebra whose center is a totally real number field. For n=1,2,3,4 and 6 it was possible to construct rotated versions of the densest lattices in their dimensions, D4,E8,K12,Λ16 and Λ24. We also present a family of lattices in dimension 2r from A=(−1,−1)Q(ζ2r +ζ2r −1) and a characterization of a maximal quaternion order of A by using the Chebyshev polynomials.en
dc.description.affiliationSão Paulo State University (UNESP), 505, Profa. Isette Corrêa Fontão avenue
dc.description.affiliationDepartment of Mathematics São Paulo State University (UNESP), 1515, 24A avenue
dc.description.affiliationIMECC University of Campinas, 651, St. Sérgio Buarque de Holanda
dc.description.affiliationUnespSão Paulo State University (UNESP), 505, Profa. Isette Corrêa Fontão avenue
dc.description.affiliationUnespDepartment of Mathematics São Paulo State University (UNESP), 1515, 24A avenue
dc.description.sponsorshipCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
dc.description.sponsorshipFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.description.sponsorshipConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.description.sponsorshipIdFAPESP: 2013/25977-7
dc.description.sponsorshipIdCNPq: 312926/2013-8
dc.identifierhttp://dx.doi.org/10.1016/j.jpaa.2019.106221
dc.identifier.citationJournal of Pure and Applied Algebra, v. 224, n. 5, 2020.
dc.identifier.doi10.1016/j.jpaa.2019.106221
dc.identifier.issn0022-4049
dc.identifier.lattes7916375574050821
dc.identifier.orcid0000-0002-4806-3399
dc.identifier.scopus2-s2.0-85072542102
dc.identifier.urihttp://hdl.handle.net/11449/197950
dc.language.isoeng
dc.relation.ispartofJournal of Pure and Applied Algebra
dc.sourceScopus
dc.subjectCenter density
dc.subjectLattices
dc.subjectMaximal orders
dc.subjectQuaternion algebras
dc.subjectSpace-time codes
dc.titleAlgebraic construction of lattices via maximal quaternion ordersen
dc.typeArtigo
unesp.author.lattes7045870107955099[2]
unesp.author.lattes7916375574050821[1]
unesp.author.orcid0000-0002-3555-392X[2]
unesp.author.orcid0000-0002-4806-3399[1]

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