中心为零的辛三代数的唯一分解

In this paper, the authors define the center of a Symplectic ternary algebra, and investigate the relationship between the center of a Symplectic ternary algebra and that of the Lie triple system associated with it. As an application of the relationship, the unique decomposition theorem for Symplectic ternary algebras with trivial center is obtained.     

Two Generator Subsystems of Lie Triple System

For a Lie triple system T over a field of characteristic zero, some sufficient conditions for T to be two-generated are proved. We also discuss to what extent the two-generated subsystems determine the structure of the system T . One of the main results is that T is solvable if and only if every two elements generates a solvable subsystem. In fact, we give an explicit two-generated law for the two-generated subsystems.     

李超三系的Frattini-子系

In the present paper,we develop initially the Frattini theory for Lie supertriple systems,obtain some properties of the Frattini subsystem and show that the intersection of all maximal subsystems of a solvable Lie supertriple system is its ideal.Moreover,we give the relationship between φ-free and complemented for Lie supertriple system.     

交换环上上三角矩阵的李三导子

Let T(n,R) be the Lie algebra consisting of all n × n upper triangular matrices over a commutative ring R with identity 1 and M be a 2-torsion free unital T(n,R)-bimodule.In this paper,we prove that every Lie triple derivation d : T(n,R) → M is the sum of a Jordan derivation and a central Lie triple derivation.     

The Frattini p-subsystem of a solvable restricted Lie triple system

As a natural generalization of a restricted Lie algebra, a restricted Lie triple system was defined by Hodge. In this paper, we develop initially the Frattini theory for restricted Lie triple systems, generalize some results of Frattini p-subalgebra for restricted Lie algebras, obtain some properties of the Frattini p-subsystem and give the relationship between Фp（T） and Ф（T） for solvable Lie triple systems.     

Some Subsystems of a Lie Triple System Closely Related to Its Frattini Subsystem

The main purpose of the present paper is to give some properties of the Jacobson radical,the Frattini subsystem and c-ideals of a Lie triple system.Some further results concerning the Frattini subsystems of nilpotent and solvable Lie triple systems are obtained.Moreover,we develop initially c-ideals for a Lie triple system and make use of them to give some characterizations of a solvable Lie triple system.     

On Split δ-Jordan Lie Triple Systems

The aim of this article is to study the structures of arbitrary split δ-Jordan Lie triple systems, which are a generalization of split Lie triple systems. By developing techniques of connections of roots for this kind of triple systems, we show that any of such δ-Jordan Lie triple systems T with a symmetric root system is of the form ■with U a subspace of T0 and any I[α] a well described ideal of T, satisfying■ .     

李三系的Killing型

For Lie triple systems in the characteristic zero setting, we obtain by means of the Killing forms two criterions for semisimplicity and for solvability respectively, and then investigate the relationship among the Killing forms of a real Lie triple system To, the complexification T of To, and the realification of T.     

On Integrable roots in split Lie triple systems

We focus on the notion of an integrable root in the framework of split Lie triple systems T with a coherent 0-root space. As a main result, it is shown that if T has all its nonzero roots integrable, then its standard embedding is a split Lie algebra having all its nonzero roots integrable. As a consequence, a local finiteness theorem for split Lie triple systems, saying that whenever all nonzero roots of T are integrable then T is locally finite, is stated. Finally, a classification theorem for split simple Lie triple systems having all its nonzero roots integrable is given.     

关于李三代数的幂零性

In this paper, we mainly concerned about the nilpotence of Lie triple algebras. We give the definition of nilpotence of the Lie triple algebra and obtained that if Lie triple algebra is nilpotent, then its standard enveloping Lie algebra is nilpotent.     

Asymptotic Estimates on the Time Derivative of Φ-entropy on Riemannian Manifolds

In this note,we obtain an asymptotic estimate for the time derivative of the Φ-entropy in terms of the lower bound of the Bakry–Emery Γ2 curvature.In the cases of hyperbolic space and the Heisenberg group(more generally,the nilpotent Lie group of rank two),we show that the time derivative of the Φ-entropy is non-increasing and concave in time t,also we get a sharp asymptotic bound for the time derivative of the entropy in these cases.     

Single-Valued Neutrosophic Lie Algebras

A single-valued neutrosophic (SVN) set is a powerful general formal framework that generalizes the concept of fuzzy set and intuitionistic fuzzy set. In SVN set, indeterminacy is quantified explicitly, and truth membership, indeterminacy membership, and falsity membership are independent. In this paper, we apply the notion of SVN sets to Lie algebras. We develop the concepts of SVN Lie subalgebras and SVN Lie ideals. We describe some interesting results of SVN Lie ideals.     

Non-abelian extensions of Lie 2-algebras

In this paper,we give the notion of derivations of Lie 2-algebras using explicit formulas,and construct the associated derivation Lie 3-algebra.We prove that isomorphism classes of non-abelian extensions of Lie 2-algebras are classified by equivalence classes of morphisms from a Lie 2-algebra to a derivation Lie 3-algebra.     

EXTENDED SYSTEMS FOR MULTIPLE S-BREAKING TURNING POINTS IN Z_2×Z_2-SYMMETRIC NONLINEAR PROBLEMS

Making use of the Z2×Z2 symmetry,we could study the structure near multiple S-treaking turning points.In particular,we show that there exist two kinds of singular point path through double S breaking turning points and triple S bieaking turning points,one ts quadratic turning pornt path and one is quadratic pitch fork bifurcation point path.Some simple regular extended systems to corn pute double and triple S-breaking turning points are proposed.Numerical examples are also green     

一类不连续系统Φ-有界变差解对参数的连续依赖性（英文）

The functions of bounded Φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper, by using Henstock-Kurzweil integral, we establish theorems of continuous dependence of bounded Φ-variation solutions on parameter for a class of discontinuous systems on the base of Φ-function. These results are essential generalizations of continuous dependence of bounded variation solutions on parameter for the systems.     

A-扩张Lie Rinehart代数

The purpose of this paper is to give a brief introduction to the category of Lie Rinehart algebras and introduces the concept of smooth manifolds associated with a unitary, commutative,associative algebra A.It especially shows that the A-extended algebra as well as the action algebra can be realized as the space of A-left invariant vector fields on a Lie group,analogous to the well known relationship of Lie algebras and Lie groups.     

NEW SUPER-HAMILTONIAN STRUCTURES OF SUPER-DIRAC HIERARCHY

In this paper, we introduce the supertrace identity and its applications. A new eight-dimensional Lie superalgebra is constructed and the super-Dirac hierarchy is derived. By the supertrace identity, we obtain the super-bi-Hamiltonian structure of the super-Dirac hierarchy.     

SUPERSYMMETRIC INVARIANCE AND UNIVERSAL CENTRAL EXTENSIONS OF LIE SUPERTRIPLE SYSTEMS

In this article, we discuss some properties of a supersymmetric invariant bilinear form on Lie supertriple systems. In particular, a supersymmetric invariant bilinear form on Lie supertriple systems can be extended to its standard imbedding Lie superalgebras. Furthermore, we generalize Garland＇s theory of universal central extensions for Lie supertriple systems following the classical one for Lie superalgebras. We solve the problems of lifting automorphisms and lifting derivations.     

Embeddings of Pure Mendelsohn Triple Systems and Pure Directed Triple Systems

A λ-fold triple system of order v,denoted TS(v,λ),is a pair(V,A)where V is a v-set and A is a collection of 3-subsets(called triples)of V such that each 2-subset of V is contained in exactly λ triples.A triple system is called simple if itcontains no repeated triples. There are two related classes of triple systems,namely,Mendelsohn triple sys-tems and directed triple systems.