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| Standardness and Standard Automorphisms of Chevalley Groups, I: the Case of Rank at Least Two |
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Citation： |
Carla BARDINI.Standardness and Standard Automorphisms of Chevalley Groups, I: the Case of Rank at Least Two[J].Chinese Annals of Mathematics B,2012,33(5):783~800 |
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Net amount： 1204 |
Authors： |
Carla BARDINI; |
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| Abstract： |
The author studies the linkage between the standardness and the standard automorphisms of Chevalley groups over rings. It is proved that if $H$ is any standard subgroup of $G(R)$, then each of its automorphisms can be extended to an automorphism of $G(R, I)$, restricted to an automorphism of $E(R, I)$, and an automorphism of $E(R, I)$ can be extended to one of $G(R, I)$. The case of Chevalley groups of rank at least two is treated in this paper. Further results about the case of Chevalley groups of rank one, the case of non-commutative ground ring and some others exceptions will appear elsewhere. |
Keywords： |
Chevalley groups, Standardness, Standard automorphism |
Classification： |
20G35, 20E36 |
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