Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective-Reference-Cited by-同舟云学术

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

Published:2016-06-01 Issue:2 Volume:24 Page:137-147
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Ceballos Manuel¹,Núñez Juan¹,Tenorio Ángel F.²

Affiliation:

1. Departamento de Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla , Spain

2. Departamento de Economía, Métodos Cuantitativos e Historia Económica, Escuela Politécnica Superior, Universidad Pablo de Olavide, Ctra. Utrera Km. 1, 41013 Sevilla , Spain

Abstract

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.

Publisher

Walter de Gruyter GmbH

Reference14 articles.

1. [1] L. Andrianopoli, R. D'Auria, S. Ferrara, P. Frè, M. Trigiante, R-R scalars, U-duality and solvable Lie algebras. Nucl. Phys. B 496 617-629 (1997).

2. [2] J.C. Benjumea, F.J. Echarte, J. Núñez and A.F. Tenorio, An Obstruction to Represent Abelian Lie Algebras by Unipotent Matrices. Extracta Math. 19 269- 277 (2004).

3. [3] J.C. Benjumea, J. Núñez and A.F. Tenorio, The Maximal Abelian Dimension of Linear Algebras formed by Strictly Upper Triangular Matrices, Theor. Math. Phys. 152 1225-1233 (2007).

4. [4] D. Burde and M. Ceballos, Abelian ideals of maximal dimension for solvable Lie algebras. J. Lie Theory 22 741-756 (2012).

5. [5] R. Campoamor-Stursberg, Number of missing label operators and upper bounds for dimensions of maximal Lie subalgebras. Acta Phys. Polon. B 37 2745-2760 (2006).