On the stability of the \(K_1\)-functor for Chevalley groups of type \(E_7\)
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).
scientific article; zbMATH DE number 1247568
scientific article