A Characterization of Linearly Semisimple Groups
نویسنده
چکیده
Let G = SpecA be an affine K-group scheme and à = {w ∈ A : dimK A ∗ · w · A < ∞}. Let 〈−,−〉 : A × Ã → K, 〈w, w̃〉 := tr(ww̃), be the trace form. We prove that G is linearly reductive if and only if the trace form is non-degenerate on A.
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