The free-lie-algebras tag has no usage guidance.

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### Poincaré-Birkhoff-Witt theorem for Leibniz algebras

Leibniz algebras can be seen as a non-skew-symmetric generalization of Lie algebras. I have already taken a look at some papers related to Leibniz algebras and extending main results of Lie algebras ...

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### Bracket of lyndon words?

Here is a simple question regarding the standard Lyndon basis for the free Lie Algebra. Suppose I take two lyndon words $m$ and $n$ and their standard bracketings $B(m)$ and $B(n)$ as elements in the ...

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### The BCH series in terms of Lyndon words

Recently I did some explicit computations that involved the BCH series, $\log(e^x e^y)$. Here $x$ and $y$ are non-commuting variables, and the BCH series lives in the graded completion $FL(x,y)$ of ...

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### About the term “tangential derivation” on a free Lie algebra.

Let $\mathcal{lie}_n$ be the free Lie algebra generated by $n$ elements $x_1,\ldots, x_n$. A derivation $u\in \text{Der}(\mathcal{lie}_n)$ is called tangential if there exist $a_i\in \mathcal{lie}_n, ...

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### list of Hall basis

Anyone know a place where the standard Hall basis is listed up to at lest
5 fold brackets?
and for gradedLie algebras?
The rules are clear but I'd rather not turn the crank myself.
Google search did ...

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### Invariant space of lifted Chevalley automorphisms of the tensor algebra

Question. Let $k$ be a field of characteristic $0$. Let $L$ be a $k$-vector space. Consider the subspace $S$ of $L\otimes L\otimes L\otimes L$ spanned by all tensors of the form
$\left[a,\left\lbrace ...