Lie algebras and separable morphisms in pro-affine algebraic groups

Nahlus, Nazih

doi:10.1090/S0002-9939-02-06963-0

Lie algebras and separable morphisms in pro-affine algebraic groups
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Proc. Amer. Math. Soc. 131 (2003), 1321-1327 Request permission

Abstract:

Let $K$ be an algebraically closed field of arbitrary characteristic, and let $f:G\rightarrow H$ be a surjective morphism of connected pro-affine algebraic groups over $K$. We show that if $f$ is bijective and separable, then $f$ is an isomorphism of pro-affine algebraic groups. Moreover, $f$ is separable if and only if (its differential) $f^o$ is surjective. Furthermore, if $f$ is separable, then ${\mathcal L}(\operatorname {Ker}f)=\operatorname {Ker} f^o$.

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