The free partially commutative Lie algebra: Bases and ranks
type: Item
instance of: scholarly article
title: The free partially commutative Lie algebra: Bases and ranks
zbMATH Open document ID: 0763.17003
DOI: 10.1016/0001-8708(92)90045-M
author: Daniel Krob
author: G. H. E Duchamp
published in: Advances in Mathematics
publication date: 1993-01-16T00:00:00Z
review text: Let \(K\) be an associative commutative ring and let \(L(A,\theta)\) be the free partially commutative Lie \(K\)-algebra over an alphabet \(A\); \(L(A,\theta)\) is the Lie algebra generated by \(A\) where the only defining relations \(\theta\) are the commutative law between some of the elements from \(A\). The main purpose of the paper under review is to show that \(L(A,\theta)\) enjoys a lot of properties of the free Lie algebra. The authors obtain a version of the Lazard elimination process, prove that \(L(A,\theta)\) is a free \(K\)-module and construct explicitly \(K\)-bases for it. They also show how the classical Witt calculus can be extended to \(L(A,\theta)\).
Mathematics Subject Classification ID: 17B01
Mathematics Subject Classification ID: 17B35
zbMATH DE Number: 94904
zbMATH Keywords: bases
zbMATH Keywords: free Lie algebra
zbMATH Keywords: Lazard elimination process
zbMATH Keywords: Witt calculus
Wikidata QID: Q115368844
reviewed by: Vesselin Drensky
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 94904