Algebraic construction of lattices via maximal quaternion orders

Detalhes bibliográficos
Autor(a) principal: Benedito, Cintya Wink de Oliveira [UNESP]
Data de Publicação: 2020
Outros Autores: Alves, Carina [UNESP], Brasil Jr, Nelson Gomes, Costa, Sueli Irene Rodrigues
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.jpaa.2019.106221
http://hdl.handle.net/11449/197950
Resumo: In 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.
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spelling Algebraic construction of lattices via maximal quaternion ordersCenter densityLatticesMaximal ordersQuaternion algebrasSpace-time codesIn 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.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)São Paulo State University (UNESP), 505, Profa. Isette Corrêa Fontão avenueDepartment of Mathematics São Paulo State University (UNESP), 1515, 24A avenueIMECC University of Campinas, 651, St. Sérgio Buarque de HolandaSão Paulo State University (UNESP), 505, Profa. Isette Corrêa Fontão avenueDepartment of Mathematics São Paulo State University (UNESP), 1515, 24A avenueFAPESP: 2013/25977-7CNPq: 312926/2013-8Universidade Estadual Paulista (Unesp)Universidade Estadual de Campinas (UNICAMP)Benedito, Cintya Wink de Oliveira [UNESP]Alves, Carina [UNESP]Brasil Jr, Nelson GomesCosta, Sueli Irene Rodrigues2020-12-12T00:54:56Z2020-12-12T00:54:56Z2020-05-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1016/j.jpaa.2019.106221Journal of Pure and Applied Algebra, v. 224, n. 5, 2020.0022-4049http://hdl.handle.net/11449/19795010.1016/j.jpaa.2019.1062212-s2.0-8507254210279163755740508210000-0002-4806-3399Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Pure and Applied Algebrainfo:eu-repo/semantics/openAccess2021-10-23T07:21:31Zoai:repositorio.unesp.br:11449/197950Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462021-10-23T07:21:31Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Algebraic construction of lattices via maximal quaternion orders
title Algebraic construction of lattices via maximal quaternion orders
spellingShingle Algebraic construction of lattices via maximal quaternion orders
Benedito, Cintya Wink de Oliveira [UNESP]
Center density
Lattices
Maximal orders
Quaternion algebras
Space-time codes
title_short Algebraic construction of lattices via maximal quaternion orders
title_full Algebraic construction of lattices via maximal quaternion orders
title_fullStr Algebraic construction of lattices via maximal quaternion orders
title_full_unstemmed Algebraic construction of lattices via maximal quaternion orders
title_sort Algebraic construction of lattices via maximal quaternion orders
author Benedito, Cintya Wink de Oliveira [UNESP]
author_facet Benedito, Cintya Wink de Oliveira [UNESP]
Alves, Carina [UNESP]
Brasil Jr, Nelson Gomes
Costa, Sueli Irene Rodrigues
author_role author
author2 Alves, Carina [UNESP]
Brasil Jr, Nelson Gomes
Costa, Sueli Irene Rodrigues
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
Universidade Estadual de Campinas (UNICAMP)
dc.contributor.author.fl_str_mv Benedito, Cintya Wink de Oliveira [UNESP]
Alves, Carina [UNESP]
Brasil Jr, Nelson Gomes
Costa, Sueli Irene Rodrigues
dc.subject.por.fl_str_mv Center density
Lattices
Maximal orders
Quaternion algebras
Space-time codes
topic Center density
Lattices
Maximal orders
Quaternion algebras
Space-time codes
description In 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.
publishDate 2020
dc.date.none.fl_str_mv 2020-12-12T00:54:56Z
2020-12-12T00:54:56Z
2020-05-01
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1016/j.jpaa.2019.106221
Journal of Pure and Applied Algebra, v. 224, n. 5, 2020.
0022-4049
http://hdl.handle.net/11449/197950
10.1016/j.jpaa.2019.106221
2-s2.0-85072542102
7916375574050821
0000-0002-4806-3399
url http://dx.doi.org/10.1016/j.jpaa.2019.106221
http://hdl.handle.net/11449/197950
identifier_str_mv Journal of Pure and Applied Algebra, v. 224, n. 5, 2020.
0022-4049
10.1016/j.jpaa.2019.106221
2-s2.0-85072542102
7916375574050821
0000-0002-4806-3399
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal of Pure and Applied Algebra
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1803046519692066816

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