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

 

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Opened Access Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective
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Author: Ceballos González, Manuel
Núñez Valdés, Juan
Tenorio Villalón, Ángel Francisco
Department: Universidad de Sevilla. Departamento de Geometría y Topología
Date: 2016
Published in: Analele Stiintifice ale Universitatii Ovidius Constanta. Seria Matematica, 24 (2), 137-148.
Document type: Article
Abstract: 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.
Cite: Ceballos González, M., Núñez Valdés, J. y Tenorio Villalón, Á.F. (2016). Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective. Analele Stiintifice ale Universitatii Ovidius Constanta. Seria Matematica, 24 (2), 137-148.
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URI: http://hdl.handle.net/11441/49657

DOI: 10.1515/auom-2016-0032

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