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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The first and the second authors are partially supported by Junta de Extremadura and FEDER funds
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Álvarez, A., Sancho, P. & Sancho, C. A characterization of linearly semisimple groups. Acta. Math. Sin.-English Ser. 27, 185–192 (2011). https://doi.org/10.1007/s10114-011-8658-1
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DOI: https://doi.org/10.1007/s10114-011-8658-1