Transitive factorizations of free partially commutative monoids and Lie algebras
Jean-Gabriel Luque, Gérard Henry Edmond Duchamp
Abstract
Let (A,θ) be a free partially commutative monoid. We give here a necessary and sufficient condition on a subalphabet B⊂ A such that the right factor of a bisection (A,θ)=(B,θ\B).T be also partially commutative free. This extends strictly the (classical) elimination theory on partial commutations and allows to construct new factorizations of (A,θ) and associated bases of L\K(A,θ).
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