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We shall describe a synthesis of results obtained by Chevalley, Kostant, Bourbaki, Demazure and myself about the construction of a group scheme associated to a semisimple complex Lie group. The method is explicit, unlike the one of Demazure (and Grothendieck). It is easy to mimic the same methods to accomodate Kac-Moody algebras and groups.
Emmanuel Ullmo