# A Characterization of Linearly Semisimple Groups - Mathematics > Algebraic Geometry

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Abstract: 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 $< -,-> : A^* \times \tilde{A}\to K, w,\tilde{w} := trw \tilde{w}$, be the trace form. We prove that $G$is linearly reductive if and only if the trace form is non-degenerate on $A^*$.

Author: ** Amelia Álvarez, Carlos Sancho, Pedro Sancho**

Source: https://arxiv.org/