Combinatorics of free pre-Lie algebras and algebras with several pre-Lie products sharing the Lie bracket

Abstract: Using the theory of algebraic operads, we give a combinatorial description of free pre-Lie algebras (also known as left-symmetric algebras) with rooted trees. A numerical coincidence hints a similar description for algebras with several pre-Lie products sharing the Lie bracket using rooted Greg trees which are rooted trees with black and white vertices such that black vertices have at least two children. We then show that those Greg trees can be used to give a description of the free Lie algebras.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar