A note on rationality of representations of profinite groups
type: Item
instance of: scholarly article
title: A note on rationality of representations of profinite groups
zbMATH Open document ID: 0901.20003
published in: Journal of Algebra
publication date: 1998-09-23T00:00:00Z
review text: Let \(G\) be a profinite group. The purpose of this note is to construct subfields \(F\) of the field of complex numbers over which a given finite dimensional complex continuous linear representation \(D\) of \(G\) is realizable in the following sense: There is a one-dimensional representation \(\mu\) of \(G\) such that \(\mu D\) is isomorphic to a linear representation which is realizable over \(F\). The proofs are based on classical results on finite linear groups and on cohomological methods.
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20E18
Mathematics Subject Classification ID: 20J05
zbMATH DE Number: 1186385
zbMATH Keywords: rationality
zbMATH Keywords: profinite groups
zbMATH Keywords: linear representations
author: Hans Opolka
reviewed by: Hans Opolka
MaRDI profile type: Publication
full work available at URL: jabr.1997.7384
OpenAlex ID: W2082046051
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DOI: 10.1006/JABR.1997.7384
description: scientific article; zbMATH DE number 1186385