Complete Lie algebras with maximal-rank nilpotent radicals  

作　　者：ZHU Linsheng and MENG Daoji Department of Mathematics, Changshu College , Changshu 215500, China  Department of Mathematics, Nankai University, Tianjin 300071, China 

出　　处：《Chinese Science Bulletin》1999年第4期312-315,共4页

摘　　要：Ccmplete Lie algebras with maximal-rank nilpotent radicals are constructed by using the representation theory of complex semisimple Lie algebras. A structure theorem and an isomorphism theorem for this kind of complete Lie algebras are obtained. As an application of these theorems, the complete Lie algebras with abelian nilpotont radicals are classified. At last, it is proved that there exists no complete Lie algebra whose radical is a nilpotent Lie algebra with maximal rank.Complete Lie algebras with maximal-rank nilpotent radicals are constructed by using the representation theory of complex semisimple Lie algebras. A structure theorem and an isomorphism theorem for this kind of complete Lie algebras are obtained. As an application of these theorems, the complete Lie algebras with abelian nilpotont radicals are classified. At last, it is proved that there exists no complete Lie algebra whose radical is a nilpotent Lie algebra with maximal rank.

关 键 词：complete LIE ALGEBRA NILPOTENT LIE ALGEBRA with MAXIMAL RANK IRREDUCIBLE module. 

分 类 号：O152.5[理学—数学]