Reductive Group
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.