The Orlik-Solomon algebra on the partition lattice and the free Lie algebra
type: Item
instance of: scholarly article
title: The Orlik-Solomon algebra on the partition lattice and the free Lie algebra
zbMATH Open document ID: 0709.17004
DOI: 10.1016/0097-3165(90)90049-3
author: Hélène Barcelo
author: Nantel Bergeron
published in: Journal of Combinatorial Theory. Series A
publication date: 1990-01-01T00:00:00Z
review text: The authors prove that the actions of the symmetric group \(S_ n\) on the exterior algebra of the free Lie algebra and on the Orlik-Solomon algebra of the partition lattice are equivalent up to tensoring with the sign representation. This is done by constructing an explicit basis in each of those spaces and creating a link between those spaces by developing a natural bijection between the constructed bases of the spaces.
Mathematics Subject Classification ID: 17B01
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 20C30
zbMATH DE Number: 4165119
zbMATH Keywords: symmetric group
zbMATH Keywords: exterior algebra
zbMATH Keywords: free Lie algebra
zbMATH Keywords: Orlik-Solomon algebra
zbMATH Keywords: partition lattice
zbMATH Keywords: representation
Wikidata QID: Q115363924
reviewed by: Melih Boral
MaRDI profile type: Publication
full work available at URL: 0097-3165(90)90049-3
OpenAlex ID: W2040054883
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cites work: On the Poincaré-Birkhoff-Witt theorem
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description: scientific article; zbMATH DE number 4165119