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
Let N be a nilpotent Lie algebra. An abelian subalgebra of DerN, whose elements are semisimple linear transformations of N, is called a torus on N. The dimension of a maximal torus H on N is called the rank of N.
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 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, ...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.展开更多
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.
In this paper, we obtain a new kind of complete Lie algebra over a commutative ring, which is the Lie algebra consisting of all n × n anti-symmetric matrices over a 2-torsionfree commutative ring with identity.
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Let N be a nilpotent Lie algebra. An abelian subalgebra of DerN, whose elements are semisimple linear transformations of N, is called a torus on N. The dimension of a maximal torus H on N is called the rank of N.
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.
文摘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.
文摘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.
文摘In this paper, we obtain a new kind of complete Lie algebra over a commutative ring, which is the Lie algebra consisting of all n × n anti-symmetric matrices over a 2-torsionfree commutative ring with identity.
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
