A remark on Baker operations on the elliptic cohomology of finite groups
type: Item
instance of: scholarly article
title: A remark on Baker operations on the elliptic cohomology of finite groups
zbMATH Open document ID: 0957.55004
author: Michimasa Tanabe
published in: Journal of Mathematics of Kyoto University
publication date: 2001-03-22T00:00:00Z
review text: Let \(G\) be a finite group and \(BG\) its classifying space. It has been known for some time that every element of \(Ell^{\text{(even)}}(BG)\) gives a certain \(p\)-adic limit of a Thompson series by applying the elliptic character. Actually rather more is true -- up to taking denominators there is an isomorphism between \(Ell^{\ast}(BG)\) and a suitably completed `elliptic representation ring'. Indeed, if the Sylow structure of \(G\) is not too complicated we can even remove the denominators. This note makes clear that the maps above are natural in the sense that the Hecke operators on representations (arising ultimately from Hecke operators on modular forms) are compatible with certain stable (Baker) operations in elliptic cohomology. This is hardly surprising, given the way in which the Baker operations are defined. Exercise: try it on cyclic groups of prime power order.
Mathematics Subject Classification ID: 55N34
Mathematics Subject Classification ID: 20J06
Mathematics Subject Classification ID: 55R35
zbMATH DE Number: 1502033
zbMATH Keywords: cohomology of groups
reviewed by: Charles B. Thomas
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250517765
OpenAlex ID: W1531110982
DOI: 10.1215/KJM/1250517765
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description: scientific article; zbMATH DE number 1502033