High Quality Content by WIKIPEDIA articles! In mathematics, a reductive group is a smooth affine algebraic group G such that the (geometric) unipotent radical of G (i.e., maximal smooth connected unipotent normal subgroup over an algebraic closure of the ground field) is trivial. Any semisimple algebraic group is reductive, as is any algebraic torus and any general linear group. The name comes from the complete reducibility of linear representations of such a group, which is a property in fact holding over fields of characteristic zero. Haboush's theorem shows that a certain rather weaker property holds for reductive groups in the general case.

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