Abstract homomorphisms between subgroups of algebraic groups were studied in detail by A.Borel, J.Tit.[1] and B.Wei.feile.[2] provided that the images of the homomorphisms are Zariski dense subsets and that the fields...Abstract homomorphisms between subgroups of algebraic groups were studied in detail by A.Borel, J.Tit.[1] and B.Wei.feile.[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 SLn(k) into SLn(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].展开更多
文摘Abstract homomorphisms between subgroups of algebraic groups were studied in detail by A.Borel, J.Tit.[1] and B.Wei.feile.[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 SLn(k) into SLn(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].
