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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Lie algebras and separable morphisms in pro-affine algebraic groups


Author: Nazih Nahlus
Journal: Proc. Amer. Math. Soc. 131 (2003), 1321-1327
MSC (2000): Primary 14L15, 16W30, 17B45, 20G15
Published electronically: December 16, 2002
MathSciNet review: 1949860
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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$.


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Additional Information

Nazih Nahlus
Affiliation: Department of Mathematics, American University of Beirut, Beirut, Lebanon
Email: nahlus@aub.edu.lb

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06963-0
PII: S 0002-9939(02)06963-0
Keywords: Lie algebras of pro-affine algebraic groups, separable morphisms
Received by editor(s): August 10, 2000
Published electronically: December 16, 2002
Communicated by: Dan M. Barbasch
Article copyright: © Copyright 2002 American Mathematical Society