Deligne's topological central extension is universal.
type: Item
instance of: scholarly article
title: Deligne's topological central extension is universal.
zbMATH Open document ID: 1037.22040
DOI: 10.1016/S0001-8708(03)00048-3
author: Gopal Prasad
published in: Advances in Mathematics
publication date: 2004-01-26T00:00:00Z
review text: Let \(F\) be a local field different from the field of complex numbers. Let \(G\) be an absolute (almost) simple, simple connected algebraic group over the field \(F\). \textit{P. Deligne} [Publ. Math., Inst. Hautes Étud. Sci. 84, 35-89 (1996; Zbl 0930.20043)] has constructed a topological central extension \[ (*) 1 \rightarrow \mu(F) \rightarrow G(F)\tilde \rightarrow G(F) \rightarrow 1. \] of \(G(F),\) where \(\mu(F)\) is a finite cyclic group of roots of identity contained in \(F\). \textit{G. Prasad} and \textit{A.S. Rapinchuk} [Publ. Math., Inst. Hautes Étud. Sci. 84, 91-187 (1996; Zbl 0941.22019)] proved that, if \(G\) is \(F\)-isotropic, then extension (*) is a universal topological central extension of \(G(F)\). This proof used global arguments. In the present paper the author gives a purely ``local'' proof of this result.
reviewed by: L. A. Kurdachenko
Mathematics Subject Classification ID: 22E55
Mathematics Subject Classification ID: 20G25
zbMATH DE Number: 2032762
zbMATH Keywords: local field
zbMATH Keywords: central extension
zbMATH Keywords: simple connected algebraic group
MaRDI profile type: Publication
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full work available at URL: s0001-8708(03)00048-3
OpenAlex ID: W1992694975
description: scientific article; zbMATH DE number 2032762