The homology of certain subgroups of the symmetric group with coefficients in \(\text{Lie}(n)\)
type: Item
instance of: scholarly article
title: The homology of certain subgroups of the symmetric group with coefficients in \(\text{Lie}(n)\)
zbMATH Open document ID: 0921.55012
DOI: 10.1016/S0022-4049(97)00050-9
author: Marja Kankaanrinta
author: Gregory Arone
published in: Journal of Pure and Applied Algebra
publication date: 1999-09-26T00:00:00Z
review text: Based on earlier work of the first author with \textit{M. Mahowald} [Invent. Math. 135, No. 3, 743--788 (1999; Zbl 0997.55016)] calculating the homology \(H_*(\Sigma_n,{\mathcal L}ie(n))\) of the symmetric group with coefficients in a certain Lie algebra over \({\mathbb Z}/p\), the authors calculate the homology of subgroups of the form \(\Sigma_{n_1} \times \cdots \times \Sigma_{n_k}\) with \(n_1+ \cdots+ n_k=n\), with the same coefficients. The approach is via homotopy theory and relies on Goodwillie's calculus of functors.
Mathematics Subject Classification ID: 55R35
Mathematics Subject Classification ID: 20J06
Mathematics Subject Classification ID: 55R40
Mathematics Subject Classification ID: 55P15
zbMATH DE Number: 1308150
zbMATH Keywords: symmetric group
zbMATH Keywords: homology
zbMATH Keywords: Lie algebra
Wikidata QID: Q115340101
reviewed by: Martin D. Crossley
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1308150