Transitive factorizations of free partially commutative monoids and Lie algebras
type: Item
instance of: scholarly article
title: Transitive factorizations of free partially commutative monoids and Lie algebras
zbMATH Open document ID: 1002.17003
DOI: 10.1016/S0012-365X(01)00253-9
author: Jean-Gabriel Luque
author: G. H. E Duchamp
published in: Discrete Mathematics
publication date: 2002-05-15T00:00:00Z
review text: The free partially commutative monoid is defined by generators and relations as \(M(A,\theta)=\langle A\mid ab=ba,\;(a,b)\in\theta\rangle\), where \(A\) is an alphabet and \(\theta\subset A\times A\) is an ``independence relation''. The case of free partially commutative Lie algebras was studied in [\textit{G. Duchamp} and \textit{D. Krob}, Adv. Math. 95, No. 1, 92-126 (1992; Zbl 0763.17003)]. The authors consider factorizations of type \(M(A,\theta)=M(B,\theta_B)\cdot T\), where \(B\subset A\) is a subalphabet. The main result is a criterion to characterize the case when \(T\) is a free partially commutative submonoid. The bases of the associated Lie algebras are constructed as well. The case of the free partially commutative group is also considered.
Mathematics Subject Classification ID: 17B01
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 20M35
Mathematics Subject Classification ID: 68Q45
zbMATH DE Number: 1741703
zbMATH Keywords: transitive monoid
zbMATH Keywords: free Lie algebra
zbMATH Keywords: Lazard elimination
zbMATH Keywords: free partially commutative monoid
reviewed by: Victor Petrogradsky
MaRDI profile type: Publication
Wikidata QID: Q114122952
full work available at URL: s0012-365x(01)00253-9
OpenAlex ID: W2950830791
description: scientific article; zbMATH DE number 1741703