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.
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.
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.
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
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.
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