Module derivations and the adjoint action of a finite loop space
type: Item
instance of: scholarly article
title: Module derivations and the adjoint action of a finite loop space
zbMATH Open document ID: 0938.55014
author: Katsuhiko Kuribayashi
published in: Journal of Mathematics of Kyoto University
publication date: 2000-06-21T00:00:00Z
review text: Let \(G\) be a loop space with the homotopy type of a finite complex. The natural adjunction map \(\text{Ad}:G\times\Omega G\to\Omega G\) gives the space \(\Omega G\times G\) a group structure which is isomorphic to the group \(LG\) of the free loops on \(G\). The aim of the paper is to give another proof of a recent result of Iwase and Kono: If \(G\) is simply connected then the following three conditions are equivalent: (i) \(H^*(G;Z)\) has no 2-torsion. (ii) \(H^*(\text{(Ad}; \mathbb{Z}/_2)= H^*(\text{pr}_2; \mathbb{Z}/_2)\) where \(\text{pr}_2\), denotes the projection of the second factor. (iii) There is an isomorphism of \(H^*(\text{BG};\mathbb{Z}/_2)\)-algebra \[ H^*(\text{BLG};\mathbb{Z}/_2)\cong H^*(\text{BG};\mathbb{Z}/_2) \otimes H^*(G; \mathbb{Z}/_2) \] which respects the inclusion onto the second factor.
Mathematics Subject Classification ID: 55P35
zbMATH DE Number: 1374923
zbMATH Keywords: free loop space
zbMATH Keywords: loop group
reviewed by: Jean-Claude Thomas
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250517954
OpenAlex ID: W1528091455
DOI: 10.1215/KJM/1250517954
description: scientific article; zbMATH DE number 1374923