Benjumea, Juan C.; Núñez, Juan; Tenorio, Ángel F. Computing the law of a family of solvable Lie algebras. (English) Zbl 1178.17002 Int. J. Algebra Comput. 19, No. 3, 337-345 (2009). Summary: This paper shows an algorithm which computes the law of the Lie algebra associated with the complex Lie group of \(n\times n\) upper-triangular matrices with exponential elements in their main diagonal. For its implementation two procedures are used, respectively, to define a basis of the Lie algebra and the nonzero brackets in its law with respect to that basis. These brackets constitute the final output of the algorithm, whose unique input is the matrix order \(n\). Besides, its complexity is proved to be polynomial and some complementary computational data relative to its implementation are also shown. Cited in 1 Document MSC: 17-08 Computational methods for problems pertaining to nonassociative rings and algebras 17B30 Solvable, nilpotent (super)algebras 68W30 Symbolic computation and algebraic computation Keywords:Solvable Lie algebra; algorithm; complexity PDF BibTeX XML Cite \textit{J. C. Benjumea} et al., Int. J. Algebra Comput. 19, No. 3, 337--345 (2009; Zbl 1178.17002) Full Text: DOI References: [1] DOI: 10.1007/s11232-007-0107-z · Zbl 1137.17302 [2] DOI: 10.1007/978-1-4612-1126-6 [3] van Est W. T., Neederl. Akad. Wetensch. Proc. A 26 pp 15– [4] Wilf H. S., Algorithms and Complexity (1986) · Zbl 0637.68006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.