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| AN EMBEDDING THEOREM BETWEEN SPECIAL LINEAR GROUPS OVER ANY FIELDS |
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Citation： |
Zha Jianguo.AN EMBEDDING THEOREM BETWEEN SPECIAL LINEAR GROUPS OVER ANY FIELDS[J].Chinese Annals of Mathematics B,1995,16(4):479~488 |
| Page view： 1037
Net amount： 886 |
Authors： |
Zha Jianguo; |
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| Abstract： |
Abstract homomorphisms between subgroups of algebraic groups were
studied in detail by A.Borel, J.Tits$^{[1]}$ and B.Weisfeiler$^{[2]}$ provided that the images
of the homomorphisms are Zariski dense subsets and that the fields over which
algebraic groups are defined are infinite. The purpose of this paper is to determine
all embedding homomorphisms of $SL_{n}(k)$ into $SL_{n}(K)$ when $k$ and $K$
are any fields of the same characteristic, without assumption of Zariski density
and infinitude of fields. The result in this paper generalizes a result of
Chen Yu on homomorphisms of two dimensional linear groups$^{[3]}$. |
Keywords： |
Classical groups, Homomorphisms, Field |
Classification： |
20G15 |
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