Noncommutativity of the group of self homotopy classes of Lie groups
type: Item
instance of: scholarly article
title: Noncommutativity of the group of self homotopy classes of Lie groups
zbMATH Open document ID: 1012.55019
DOI: 10.1016/S0166-8641(01)00261-9
author: Martin Arkowitz
author: Hideaki Ōshima
author: Jeffrey Strom
published in: Topology and its Applications
publication date: 2003-03-10T00:00:00Z
review text: Let \(G\) be a topological group and let \([G,G]\) be the group of homotopy classes of self maps of \(G\). The main result of the paper is that if \(G\) is \(\text{SU}(n)\) for \(n>2\), or \(\text{Sp}(n)\) for \(n>1\), or \(\text{Spin}(4n)\) for \(n>1\), and if \(H\) is a central subgroup of \(G\), then \([G/H,G/H]\) is not commutative. This extends some earlier results of two of the authors. Furthermore, for certain Lie groups \(G\), they show that nil \([G,G] >2\).
Mathematics Subject Classification ID: 55Q05
Mathematics Subject Classification ID: 57T20
zbMATH DE Number: 1879112
zbMATH Keywords: Lie group
zbMATH Keywords: self homotopy class
zbMATH Keywords: nilpotency class
reviewed by: C. S. Hoo
Wikidata QID: Q115339623
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1879112