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
Descripción
Sumario: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.