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Minimal faithful upper-triangular matrix representations for solvable Lie algebras

 

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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: 2017-07
Published in: Journal of Computational and Applied Mathematics, 318, 279-292.
Document type: Article
Abstract: A well-known result on Lie Theory states that every finite-dimensional complex solvable Lie algebra can be represented as a matrix Lie algebra, with upper-triangular square matrices as elements. However, this result does not specify which is the minimal order of the matrices involved in such representations. Hence, the main goal of this paper is to revisit and implement a method to compute both that minimal order and a matrix representative for a given solvable Lie algebra. As application of this procedure, we compute representatives for each solvable Lie algebra with dimension less than 6.
Cite: Ceballos González, M., Núñez Valdés, J. y Tenorio Villalón, Á.F. (2017). Minimal faithful upper-triangular matrix representations for solvable Lie algebras. Journal of Computational and Applied Mathematics, 318, 279-292.
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URI: http://hdl.handle.net/11441/53484

DOI: 10.1016/j.cam.2016.09.015

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