On the Bases of a Free Lie Algebra

Abstract

In the work of M. Hall [1], a certain way of fixing a basis of a free Lie algebra is indicated. However, the concrete bases which one needs to construct, in order to solve certain problems, do not always fall into Hall’s scheme. For instance, the basis of a free Lie algebra considered in the work [2] cannot be constructed using Hall’s method. For this reason, in each such case it is necessary to reprove that a certain subset of a free Lie algebra is a basis. Below, we give a method that generalizes Hall’s method for choosing a basis in a free Lie algebra.