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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Detalhes bibliográficos
Autores: Ceballos González, Manuel, Núñez Valdés, Juan, Tenorio Villalón, Ángel Francisco
Formato: artículo
Fecha de publicación:2016
País:España
Recursos:Universidad Loyola Andalucía
Repositorio:Brújula
OAI Identifier:oai:repositorio.uloyola.es:20.500.12412/1143
Acesso em linha:http://hdl.handle.net/20.500.12412/1143
Access Level:acceso abierto
Palavra-chave:Maximal abelian dimension
Solvable Lie algebra
Algorithm
Descrição
Resumo: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.