On the (co)homology of the partition lattice and the free Lie algebra.
type: Item
instance of: scholarly article
title: On the (co)homology of the partition lattice and the free Lie algebra.
zbMATH Open document ID: 1061.05513
DOI: 10.1016/S0012-365X(98)00147-2
author: Michelle L. Wachs
published in: Discrete Mathematics
publication date: 2000-11-02T00:00:00Z
review text: We explore the well-known relationship between the representations of the symmetric group on the homology of the partition lattice and on the \(l^n\) component of the free Lie algebra. We give two new combinatorial proofs of the sign twisted isomorphism between the two modules. One involves a bijection between bases and the other involves a bijection between generating sets which takes relations to relations.
Mathematics Subject Classification ID: 05E25
Mathematics Subject Classification ID: 17B01
Mathematics Subject Classification ID: 20C30
zbMATH DE Number: 1525039
zbMATH Keywords: symmetric group
zbMATH Keywords: partition lattice
zbMATH Keywords: free Lie algebra
Wikidata QID: Q115340636
MaRDI profile type: Publication
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full work available at URL: s0012-365x(98)00147-2
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description: scientific article; zbMATH DE number 1525039