Isomorphisms of Chevalley groups over algebras
type: Item
instance of: scholarly article
title: Isomorphisms of Chevalley groups over algebras
zbMATH Open document ID: 0957.20029
author: Yu Chen
published in: Journal of Algebra
publication date: 2000-12-14T00:00:00Z
review text: The aim of this paper is to characterize the automorphisms and isomorphisms of Chevalley groups over \(\mathbb{Q}\)-algebras without zero divisors. It is based on an earlier work of the author [Tôhoku Math. J., II. Ser. 47, No. 1, 81-97 (1995; Zbl 0829.20070)]. Let \(G\) be an almost simple Chevalley-Demazure group scheme of rank greater than 1, and \(R\) a commutative \(\mathbb{Q}\)-algebra without zero divisors. The author proves that any automorphism of \(G(R)\) is ``standard'' in some sense. Let \(G\) and \(G'\) be Chevalley-Demazure group schemes containing no simple component of type \(A_1\), and let \(R\) and \(R'\) be commutative \(\mathbb{Q}\)-algebras without zero divisors. The author proves that, if \(G\) is simply connected, then any isomorphism from \(G(R)\) onto \(G'(R')\) is ``standard''. The problem to determine the isomorphisms of Chevalley groups of type \(A_1\) is more complicated and is still open.
Mathematics Subject Classification ID: 20G35
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20H25
Mathematics Subject Classification ID: 14L15
zbMATH DE Number: 1448608
zbMATH Keywords: Chevalley groups
zbMATH Keywords: standard isomorphisms
zbMATH Keywords: standard automorphisms
zbMATH Keywords: almost simple Chevalley-Demazure group schemes
MaRDI profile type: Publication
full work available at URL: jabr.1999.8133
OpenAlex ID: W1973484827
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DOI: 10.1006/JABR.1999.8133
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description: scientific article; zbMATH DE number 1448608