Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective

In this paper, the maximal abelian dimension is algorithmically and computationally studied for the Lie algebra hn, of n×n upper-triangular matrices. More concretely, we define an algorithm to compute abelian subalgebras of hn besides programming its implementation with the symbolic computation pack...

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Detalles Bibliográficos
Autores: Ceballos González, Manuel, Núñez Valdés, Juan, Tenorio Villalón, Ángel Francisco
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2016
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/49657
Acceso en línea:http://hdl.handle.net/11441/49657
https://doi.org/10.1515/auom-2016-0032
Access Level:acceso abierto
Palabra clave:Maximal abelian dimension
Solvable Lie algebra
Algorithm
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spelling Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspectiveCeballos González, ManuelNúñez Valdés, JuanTenorio Villalón, Ángel FranciscoMaximal abelian dimensionSolvable Lie algebraAlgorithmIn this paper, the maximal abelian dimension is algorithmically and computationally studied for the Lie algebra hn, of n×n upper-triangular matrices. More concretely, we define an algorithm to compute abelian subalgebras of hn besides programming its implementation with the symbolic computation package MAPLE. The algorithm returns a maximal abelian subalgebra of hn and, hence, its maximal abelian dimension. The order n of the matrices hn is the unique input needed to obtain these subalgebras. Finally, a computational study of the algorithm is presented and we explain and comment some suggestions and comments related to how it works.Ovidius UniversityGeometría y TopologíaFQM326: Geometría Diferencial y Teoría de Lie2016info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/49657https://doi.org/10.1515/auom-2016-0032reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésAnalele Stiintifice ale Universitatii Ovidius Constanta. Seria Matematica, 24 (2), 137-148.http://www.anstuocmath.ro/mathematics//ANALE2016VOL2/Ceballos_M.__Nunez_J.__Tenorio_A.F..pdfinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/496572026-06-17T12:51:07Z
dc.title.none.fl_str_mv Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective
title Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective
spellingShingle Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective
Ceballos González, Manuel
Maximal abelian dimension
Solvable Lie algebra
Algorithm
title_short Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective
title_full Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective
title_fullStr Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective
title_full_unstemmed Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective
title_sort Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective
dc.creator.none.fl_str_mv Ceballos González, Manuel
Núñez Valdés, Juan
Tenorio Villalón, Ángel Francisco
author Ceballos González, Manuel
author_facet Ceballos González, Manuel
Núñez Valdés, Juan
Tenorio Villalón, Ángel Francisco
author_role author
author2 Núñez Valdés, Juan
Tenorio Villalón, Ángel Francisco
author2_role author
author
dc.contributor.none.fl_str_mv Geometría y Topología
FQM326: Geometría Diferencial y Teoría de Lie
dc.subject.none.fl_str_mv Maximal abelian dimension
Solvable Lie algebra
Algorithm
topic Maximal abelian dimension
Solvable Lie algebra
Algorithm
description In this paper, the maximal abelian dimension is algorithmically and computationally studied for the Lie algebra hn, of n×n upper-triangular matrices. More concretely, we define an algorithm to compute abelian subalgebras of hn besides programming its implementation with the symbolic computation package MAPLE. The algorithm returns a maximal abelian subalgebra of hn and, hence, its maximal abelian dimension. The order n of the matrices hn is the unique input needed to obtain these subalgebras. Finally, a computational study of the algorithm is presented and we explain and comment some suggestions and comments related to how it works.
publishDate 2016
dc.date.none.fl_str_mv 2016
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/49657
https://doi.org/10.1515/auom-2016-0032
url http://hdl.handle.net/11441/49657
https://doi.org/10.1515/auom-2016-0032
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Analele Stiintifice ale Universitatii Ovidius Constanta. Seria Matematica, 24 (2), 137-148.
http://www.anstuocmath.ro/mathematics//ANALE2016VOL2/Ceballos_M.__Nunez_J.__Tenorio_A.F..pdf
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Ovidius University
publisher.none.fl_str_mv Ovidius University
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
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repository.mail.fl_str_mv
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