Lie algebras and separable morphisms in pro-affine algebraic groups
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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 ${\mathcal L}(\operatorname {Ker}f)=\operatorname {Ker} f^o$.References
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Additional Information
- Nazih Nahlus
- Affiliation: Department of Mathematics, American University of Beirut, Beirut, Lebanon
- Email: nahlus@aub.edu.lb
- Received by editor(s): August 10, 2000
- Published electronically: December 16, 2002
- Communicated by: Dan M. Barbasch
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1321-1327
- MSC (2000): Primary 14L15, 16W30, 17B45, 20G15
- DOI: https://doi.org/10.1090/S0002-9939-02-06963-0
- MathSciNet review: 1949860