A Characterization of Linearly Semisimple Groups

Abstract

Let $G=SpecA$ be an affine $K$-group scheme and $\tilde{A}=\{w\in A\ast :di{m}_K{A}^{\ast }\cdot w\cdot A^{\ast }<\infty \}$. Let $<-,->:A^{\ast }\times \tilde{A}\to K,(w,\tilde{w}):=tr(w\tilde{w})$, be the trace form. We prove that $G$ is linearly reductive if and only if the trace form is non-degenerate on $A^{\ast }$.

References in corpus (1)

• Reynolds Operator on functors