On the stability of the \(K_1\)-functor for Chevalley groups of type \(E_7\)
type: Item
instance of: scholarly article
title: On the stability of the \(K_1\)-functor for Chevalley groups of type \(E_7\)
zbMATH Open document ID: 0918.20039
author: K. Appert
published in: Journal of Algebra
publication date: 1999-06-15T00:00:00Z
review text: Let \(R\) be a commutative ring with 1, \(G(E_7,R)\) the Chevalley-Demazure group of type \(E_7\), and \(E(E_7,R)\) the subgroup generated by the root elements. Theorem 1 asserts that \(G(E_7,R)=G(E_6,R)E(E_7,R)\) when the maximal spectrum of \(R\) is of dimension at most 4. Theorem 2 asserts the same under more complicated conditions. Theorem 3 asserts that \(G(E_6,R)=G(D_5,R)E(E_6,R)\) under similar conditions. (Also submitted to MR).
Mathematics Subject Classification ID: 20G35
Mathematics Subject Classification ID: 19B14
zbMATH DE Number: 1247568
zbMATH Keywords: stability
zbMATH Keywords: Chevalley groups
zbMATH Keywords: root elements
reviewed by: L. N. Vaserstein
MaRDI profile type: Publication
full work available at URL: jabr.1998.7535
OpenAlex ID: W2036061945
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DOI: 10.1006/JABR.1998.7535
description: scientific article; zbMATH DE number 1247568