A Characterization of Linearly Semisimple Groups

Details A Characterization of Linearly Semisimple Groups A Characterization of Linearly Semisimple Groups

2009-08-31

arxiv.org/abs/0908.4482v1

Mathematics

Algebraic Geometry

Scientific paper

Let $G = Spec A$ be an affine $K$-group scheme and $\tilde{A} = \{w \in A*:
dim_K A^* \cdot w \cdot A^* < \infty \}$. Let $< -,-> : A^* \times \tilde{A}
\to K, (w,\tilde{w}) := tr(w \tilde{w})$, 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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