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 perspective Ceballos González, Manuel Núñez Valdés, Juan Tenorio Villalón, Ángel Francisco Maximal abelian dimension Solvable Lie algebra Algorithm 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. Ovidius University http://hdl.handle.net/11441/49657 https://doi.org/10.1515/auom-2016-0032
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
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
topic Maximal abelian dimension
Solvable Lie algebra
Algorithm
topic_facet 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
format article
status_str publishedVersion
url http://hdl.handle.net/11441/49657
https://doi.org/10.1515/auom-2016-0032
eu_rights_str_mv openAccess
publisher Ovidius University
institution Universidad de Sevilla (US)
collection idUS. Depósito de Investigación de la Universidad de Sevilla
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
instname_str Universidad de Sevilla (US)
_version_ 1878443402526195712
publishDateSort 2016
author_browse Ceballos González, Manuel
Núñez Valdés, Juan
Tenorio Villalón, Ángel Francisco
publisherStr Ovidius University
score 6.9303427

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