Computational calculus of the law of a family of solvable Lie algebras

Article type: Research Article

Authors: Benjumea, J.C.^a | Morales, M.D.^a | Núñez, J.^{a; *} | Tenorio, A.F.^b

Affiliations: [a] Dpto. Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, Sevilla, Spain | [b] Dpto. Métodos Cuantitativos, Escuela Politécnica Superior, Universidad Pablo de Olavide, Sevilla, Spain

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: This paper studies the law of the Lie algebras hn associated with a particular type of Lie groups: the Lie groups Hn formed by all the n×n upper-triangular matrices without zeros in their main diagonal. Indeed, these laws are obtained by means of a computational algorithm which we have constructed and particularly implemented by using the symbolic computation package MAPLE. Besides, the complexity of this algorithm is studied by considering the number of computations carried out with this implementation.

Keywords: Solvable Lie algebra, MAPLE, algorithmic procedure, computer algebra

DOI: 10.3233/JCM-2012-0397

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 12, no. 3, pp. 189-198, 2012