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...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.展开更多
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...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 nilpotent Lie algebras.展开更多
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 complet...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.展开更多
THE theory of nilpotent Lie algebra is very important in the theory of finite-dimensional Lie al-gebras. Because of its extraordinary complexity, one usually studies various classes of specialnilpotent Lie algebras. I...THE theory of nilpotent Lie algebra is very important in the theory of finite-dimensional Lie al-gebras. Because of its extraordinary complexity, one usually studies various classes of specialnilpotent Lie algebras. In the study of complete Lie algebras, a class of special nilpotent Lie al-gebras (called completable nilpotent Lie algebras) was discovered. In this letter, we will展开更多
基金Project supported by the the National Natural Science Foundation of China (No. 19971044) the Doctoral Program Foundation of the Ministry of Education of China (No. 97005511).
文摘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.
基金Supported by National Science Foundation of Jiangau.
文摘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 nilpotent Lie algebras.
文摘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.
文摘THE theory of nilpotent Lie algebra is very important in the theory of finite-dimensional Lie al-gebras. Because of its extraordinary complexity, one usually studies various classes of specialnilpotent Lie algebras. In the study of complete Lie algebras, a class of special nilpotent Lie al-gebras (called completable nilpotent Lie algebras) was discovered. In this letter, we will
