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

This paper studies the law of the Lie algebras h n associated with a particular type of Lie groups: the Lie groups H n 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.