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complete lie algebraS WITH l-STEP NILPOTENT RADICALS

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Chinese Annals of Mathematics,Series B 2002年第4期23卷 545-550页

作者： GAOYONGCUN MENGDAOJI DepartmentofMathematics BeijingBroadcastingInstituteBeijing100024China. DepartmentofMathematics NankaiUniversityTianjin300071China.

The authors first give a necessary and sufficient condition for some solvable lie algebras with l-step nilpotent radicals to be complete, and then construct a new class of infinite dimensional complete lie algebras by using the modules of simple lie algebras. The quotient algebras of this new constructed lie algebras are non-solvable complete lie algebras with l-step nilpotent radicals.

关键词： complete lie algebra l-step nilpotent lie algebra Nilpotent radical

Two Kinds of Solvable complete lie algebras

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Chinese Quarterly Journal of Mathematics 1996年第3期11卷 59-66页

作者：朱林生 Dept.of Math. Changshu College Changshu 215500 Jiangsu China

In this paper,we will give the definition of completable nilpotent lie algebras,discuss its decomposition and prove that the heisenberg algebras and extensions of abelian quadratic lie algebras are all completable nil... 详细信息

关键词： complete lie algebra Heisenberg algebra abclian reqular quadratic lie algebra

The Classification and Realization of complete liealgebras with Commutative Nilpotent Radicals

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Northeastern Mathematical Journal 1998年第1期14卷 34-40页

作者：朱林生

in this paper, the classification and realization of complete lie algebras withcommutative nilpotent radicals are given. From this, some results on the radicals of thesecomplete lie algebras are obtained.

关键词： complete lie algebra Nilpotent Radical Irreducible Module

Derivation algebra of Quasi R_n-filiform lie algebra

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Communications in Mathematical Research 2012年第3期28卷 218-224页

作者： Wu MING-EHONG Department of Mathematics China West Normal University Nanchong Sichuan 637000

In this paper we explicitly determine the derivation algebra of a quasi Rn-filiform lie algebra and prove that a quasi Rn-filiform lie algebra is a completable nilpotent lie algebra.

关键词： filiform lie algebra complete lie algebra derivation algebra

The lie algebras in which Every Subspace Is Its Subalgebra

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Communications in Mathematical Research 2009年第1期25卷 1-8页

作者： Wu MING-ZHONG Liu Jian-ya Department of Mathematics China West Normal University Nanchong 637002

In this paper, we study the lie algebras in which every subspace is its subalgebra （denoted by HB lie algebras）. We get that a nonabelian lie algebra is an HB lie algebra if and only if it is isomorphic to g＋Cidg, where g is an abelian lie algebra. Moreover we show that the derivation algebra and the holomorph of a nonabelian HB lie algebra are complete.

关键词： HB lie algebra complete lie algebra holomorph