A computational study of a family of nilpotent Lie algebras

This paper describes an algorithm to compute the law of the Lie algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak{g}_{n}$\end{document} associated with the Lie group Gn, formed of all the n×n upper-unitriangular matrices. The goal of this paper is to show the algorithm that computes the law of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak{g}_{n}$\end{document} and its implementation using the symbolic computation package MAPLE. In addition, the complexity of the algorithm is described.