I am currently working with the set of commutators of $A$ and $B$. Due to special properties of these, I am interested in working with a basis of these commutators (due to anticommutativity, not all possible commutators are needed for a description of a given problem).
$n=1$: $A$, $B$
$n=2$: $[A,B]$
$n=3$: $[A,[A,B]]$, $[[A,B],B]$
and so on (in a complicated way ;))
This set is called a "Lyndon basis" for a free Lie algebra generated by $A$ and $B$, if I am not mistaken.
I should do some research on the term "Dynkin basis", which should refer to a basis of the form $[\cdot, [\cdot, [\cdots ]\cdots]]$. Can someone point out good literature to work with, especially for establishing connections to the previously mentioned context with Lyndon basis, if there is any? I did not cover any course on Lie algebras. Is there a way for getting to the point quickly?