Abstract
Many attempts have been made to describe bases for the post-Lie algebra, using many types of Lie bases. Here, we try to describe special kind of post-Lie bases using those bases described in the pre-Lie (respectively Lie) contexts, founded before in [8, 9]. In addition, we try to understand the effect of the second operation of the post-Lie structure on the form of these bases, using some cases of the generating set, and translate it in terms of rooted trees.
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