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Fabien Morel

Presentations of groups of points of split semi-simple algebraic groups over polynomial rings


Abstract. Let G be a split semi-simple group over a field K. We reformulate classical results concerning presentation of the group G(K) and we then extend these results to a presentation of the groups of the form G(A) with A = K[X_1,..,X_n]. This extends results of Soule (n = 1). We show how these presentations may be used to establish the homotopy invariance of group homology in new cases.

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