1.

The Frattini psubsystem of a solvable restricted Lie triple system





Liang Yun Chen Dong Liu《数学学报(英文版)》,2010年第26卷第10期


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 psubalgebra for restricted Lie algebras, obtain some properties of the Frattini psubsystem and give the relationship between Фp（T） and Ф（T） for solvable Lie triple systems.

2.

关于Hom李代数的结构





王圣祥 张晓辉《数学研究及应用》,2014年第34卷第4期


Let A be a multiplicative Homassociative algebra and L a multiplicative HomLie algebra together with surjective twisting maps. We show that if A is a sum of two commutative Homassociative subalgebras, then the commutator Homideal is nilpotent. Furthermore, we obtain an analogous result for HomLie algebra L extending Kegel＇s Theorem. Finally, we discuss the HomLie ideal structure of a simple Homassociative algebra A by showing that any noncommutative HomLie ideal of A must contain [A, A].

3.

超交换环上的一般线性李超代数的极大阶化子代数





李杨 刘文德《数学研究及应用》,2015年第35卷第2期


In this paper, we determine all maximal graded subalgebras of the general linear Lie superalgebras containing the standard Cartan subalgebras over a unital supercommutative superring with 2 invertible.

4.

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





Liangyun CHEN Dong LIU Xiaoning XU《数学年刊B辑(英文版)》,2013年第34卷第5期


The main purpose of the present paper is to give some properties of the Jacobson radical,the Frattini subsystem and cideals 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 cideals for a Lie triple system and make use of them to give some characterizations of a solvable Lie triple system.

5.

辛代数的极大幂零子代数的保李括积零的线性映射





赵延霞 王登银 贾东芳《数学研究及应用》,2011年第31卷第5期


Let F be a field with char F = 2, l a maximal nilpotent subalgebra of the symplectic algebra sp（2m,F）. In this paper, we characterize linear maps of l which preserve zero Lie brackets in both directions. It is shown that for m ≥ 4, a map φ of l preserves zero Lie brackets in both directions if and only if φ = ψcσT0λαφdηf, where ψc,σT0,λα,φd,ηf are the standard maps preserving zero Lie brackets in both directions.

6.

Engel Subalgebras of nLie Algebras





Donald W. BARNES《数学学报(英文版)》,2008年第24卷第1期


Engel subalgebras of finitedimensional nLie algebras are shown to have similar properties to those of Lie algebras. Using these, it is shown that an nLie algebra, all of whose maximal subalgebras are ideals, is nilpotent. A primitive 2soluble nLie algebra is shown to split over its minimal ideal, and all the complements to its minimal ideal are conjugate. A subalgebra is shown to be a Cartan subalgebra if and only if it is minimal Engel, provided that the field has sufficiently many elements. Cartan subalgebras are shown to have a property analogous to intravariance.

7.

关于Malcev代数的幂零性





张知学 冯建强《东北数学》,2005年第21卷第1期


We investigate the nilpotence of a Malcev algebra M and of its standard enveloping Lie algebra L(M)=M D(M, M). The main result shows that an ideal A of M is nilpotent in M if and only if the corresponding ideal Ⅰ(A) = A D(A, M)is nilpotent in L(M).

8.

2Local Automorphisms on Basic Classical Lie Superalgebras





Li YU Ying WANG Hai Xian CHEN Ji Zhu NAN《数学学报(英文版)》,2019年第3期


Let G be a basic classical Lie superalgebra except A(n, n) and D(2, 1, α) over the complex number field C. Using existence of a nondegenerate invariant bilinear form and root space decomposition, we prove that every 2local automorphism on G is an automorphism. Furthermore, we give an example of a 2local automorphism which is not an automorphism on a subalgebra of Lie superalgebra spl(3, 3).

9.

nLie代数的Frattini子代数及非嵌入定理





白瑞蒲 周和月 刘学文《东北数学》,2006年第22卷第4期


In this paper,we prove the nonimbedding theorem in nilpotent nLiealgebras which is an analogue to the nonimbedding theorem of Burnsids in groupsof prime power order.We also study the properties of Frattini subalgebras of nLiealgebras over the field with characteristic zero,and prove that the Frattini subalgebraof any ksolvable(k≥2)nLie algebra is zero.

10.

Quadratic Lie Superalgebras Generalized by Balinsky–Novikov Superalgebras





Yi TAO Zhi Qi CHEN Yan WANG《数学学报(英文版)》,2019年第2期


Balinsky–Novikov superalgebras were introduced by Balinsky for constructing superVirasoro type Lie superalgebras. In this paper, we give sufficient and necessary conditions for a Lie superalgebra generalized by a Balinsky–Novikov superalgebra with dimension 22 to be a quadratic Lie superalgebra.

11.

On Restricted Lie Superalgebras with Semisimple Elements





陈良云 孟道骥《东北数学》,2005年第21卷第3期


In the present paper, we give some sufficient conditions for the commu tativity of restricted Lie superalgebras and characterize some properties of restricted Lie superalgebras with semisimple elements.

12.

关于完满的Lie超代数 被引次数：1





张润萱 陈良云 张永正《东北数学》,2008年第24卷第6期


In this paper, some properties of perfect Lie superalgebras are investigated. We prove that the derivation superalgebra of a centerless perfect Lie superalgebra of arbitrary dimension over a field of arbitrary characteristic is complete and we obtain a necessary and sufficient condition for the holomorph of a centerless perfect Lie superalgebra to be complete. Finally, some properties of perfect restricted Lie superalgebras are given.

13.

李超三系的Frattini子系 被引次数：1





吴险峰 陈良云《数学研究及应用》,2010年第30卷第3期


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 φfree and complemented for Lie supertriple system.

14.

EMBEDDING THEOREM OF FILTERED LIE SUPERALGEBRAS





张永正 沈光宁《数学物理学报(B辑英文版)》,2001年第3期


In recent years the Lie superalgebras have become a 8ubject of intere8t in both mathematicsand physic8['][41. We know that the embedding theorems of Zgraded Lie superalgebras andfiltered Lie superalgebras play an important role in the investigation of Lie superalgebras. Theembedding theorem of Zgreded Lie superalgebras is already proved in paper [5l. In this paperthe homomorphic realization Of Lie superalgebras is given and proved by tlle method of tlieReff6]. Using the result of honro…

15.

RESEARCH ANNOUNCEMENTS——Structure of Solvable Quadratic Lie Algebras





朱林生《数学进展》,2005年第34卷第1期


Killing form plays a key role in the theory of semisimple Lie algebras. It is natural to extend the study to Lie algebras with a nondegenerate symmetric invariant bilinear form. Such a Lie algebra is generally called a quadratic Lie algebra which occur naturally in physics^[10，12，13]. Besides semisimple Lie algebras, interesting quadratic Lie algebras include the KacMoody algebras and the Extended Affine Lie algebras. In this paper, we study solvable quadratic Lie algebras. In Section 1, we study quadratic solvable Lie algebras whose Cartan subalgebras consist of semisimple elements. In Section 2,we present a procedure to construct a class of quadratic Lie algebras, and we can exhaust all solvable quadratic Lie algebras in such a way. All Lie algebras mentioned in this paper are finite dimensional Lie algebras over a field F of characteristic 0.

16.

OmniLie superalgebras and Lie 2superalgebras





Tao Zhang Zhangju Liu《Frontiers of Mathematics in China》,2014年第9卷第5期


We introduce the notion of omniLie superalgebras as a super version of an omniLie algebra introduced by Weinstein. This algebraic structure gives a nontrivial example of Leibniz superalgebras and Lie 2superalgebras. We prove that there is a onetoone correspondence between Dirac structures of the omniLie superalgebra and Lie superalgebra structures on a subspace of a super vector space,

17.

Linear Commuting Maps on Parabolic Subalgebras of Finitedimensional Simple Lie Algebras





CHEN Zhengxin WANG Bing《数学季刊》,2014年第4期


A map φ on a Lie algebra g is called to be commuting if [φ（x）,x] = 0 for all x ∈ g. Let L be a finitedimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear map φ on P is commuting if and only if φ is a scalar multiplication map on P.

18.

adNILPOTENT ELEMENTS, QUASINILPOTENT ELEMENTS AND INVARIANT FILTRATIONS OF INFINITE DIMENSIONAL LIE ALGEBRAS OF CARTAN TYPE





金宁《中国科学B辑(英文版)》,1992年第10期


Let F be an arbitrary field of characteristic p≠2, and L be an infinite Lie, algebra ofCartan type (graded or complete). When p>3 (or p is arbitrary), the set of adnilpotent(or quasinilpotent) elements of L is determined. Consequently, it is proved that the naturalfiltration and the noncontractible filtration of L are invariant.

19.

On the Classification of Finite RTrivial PSemigroups





朱聘瑜《数学进展》,1989年第1期


In this paper we discuss the classification of finite RtriVial Psemigroups (congruence permutable semigroup).It is clear that the monogenic semigroup C_(n,1)and c_(n,1)~1 are RtriVial PsemigYoups.F01"the Proper ideal R={a~k,a~(k ),…a~k of C_(n,1)~1,the branehextension[4]C_(n,1)~1×I/R is a Psereigroup,denoted by C_(x,1,k)~1 It is a RtriVial semigroulp. Let N be the set of nattlral nulnbers,l≠s∈N,e_l,e_2,a are transfotmations of

20.

有限群的$p$覆盖远离子群及$S$拟正规嵌入子群





何宣丽 王燕鸣《数学研究及应用》,2010年第30卷第4期


Let G be a finite group, p the smallest prime dividing the order of G and P a Sylow psubgroup of G. If d is the smallest generator number of P, then there exist maximal subgroups P1, P2,..., Pd of P, denoted by Md（P） = {P1,...,Pd}, such that di=1 Pi = Φ（P）, the Frattini subgroup of P. In this paper, we will show that if each member of some fixed Md（P） is either pcoveravoid or Squasinormally embedded in G, then G is pnilpotent. As applications, some further results are obtained.
