A computational study of a family of nilpotent Lie algebras

This paper describes an algorithm to compute the law of the Lie algebra \(\mathfrak{g}_{n}\) 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 \(\mathfrak{g}_{n}\) and its implementation using the symbolic computation package MAPLE. In addition, the complexity of the algorithm is described.