A characterization of linearly semisimple groups |
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| Authors: | Amelia Álvarez Pedro Sancho Carlos Sancho |
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| Affiliation: | (1) Department of Mathematics, University of Ottawa, Ottawa, ON, Canada;(2) School of Computer Science, McGill University, Montreal, QC, Canada |
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| Abstract: | Let G = SpecA be an affine K-group scheme and à = {w ∈ A*: dim K A*·w < ∞, dim K w· A* < ∞}. Let 〈?,?〉: A* × Ã → K, 〈w, (tilde w)〉:=tr(w~w), 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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| Keywords: | Linearly reductive group trace form Pontrjagin＇s duality |
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