On the stability of the \(K_1\)-functor for Chevalley groups of type \(E_7\) (Q1276978)
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scientific article; zbMATH DE number 1247568
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the stability of the \(K_1\)-functor for Chevalley groups of type \(E_7\) |
scientific article; zbMATH DE number 1247568 |
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On the stability of the \(K_1\)-functor for Chevalley groups of type \(E_7\) (English)
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15 June 1999
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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).
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stability
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Chevalley groups
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root elements
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