Séminaire Lotharingien de Combinatoire, B54k (2006), 19 pp.

Gérard Duchamp, Marianne Flouret and Jean-Gabriel Luque

Transitive Hall Sets

Abstract. We give the definition of Lazard and Hall sets in the context of transitive factorizations of free monoids. The equivalence of the two properties is proved. This allows to build new effective bases of free partially commutative Lie algebras. The commutation graphs for which such sets exist are completely characterized and we explicit, in this context, the classical PBW rewriting process.

Received: June 30, 2005. Revised: May 26, 2006. Accepted: July 7, 2006.

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