Résumé : In this talk, we generalize the classical Lazard’s elimination on the free Lie algebra L_k(X) to a more general scheme, namely quotients of Lazard’s eliminations. This implies (for Lie algebras defined by generators and relations) situations when the alphabet of generators can be partitioned in a way compatible with the relations. In this case, our scheme provides semidirect decompositions of these Lie algebras. As particular cases we consider the Partially Commutative Lie algebras and Drinfeld-Kohno Lie algebras for which our result provides decompositions of the Lie algebras (of these two series) into direct sums of free Lie algebras. As a result, we indicate how to construct combinatorial bases (of these Lie algebras) and their dual bases. Incidentally, we recover answers to Pr. Schützenberger’s questions about the Partially Commutative Free Lie algebra.

 [Slides.pdf] [vidéo]

Dernière modification : Monday 27 May 2024

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