1.

HomGel'fand–Dorfman Superbialgebras and HomLie Conformal Superalgebras





La Mei Yuan Sheng Chen Cai Xia He《数学学报(英文版)》,2017年第33卷第1期


The aim of this paper is to introduce and study HomGel'fand–Dorfman superbialgebras and HomLie conformal superalgebras. In this paper, we provide different ways for constructing HomGel'fand–Dorfman superbialgebras. Also, we obtain some infinitedimensional HomLie superalgebras from affinization of HomGel'fand–Dorfman superbialgebras. Finally, we give a general construction of HomLie conformal superalgebras from HomLie superalgebras and establish the equivalence between quadratic HomLie conformal superalgebras and HomGel'fand–Dorfman superbialgebras.

2.

Dirac Operators on Quadratic Lie Superalgebras





《数学学报(英文版)》,2021年第8期


Assume that r is a finite dimensional complex Lie superalgebra with a nondegenerate supersymmetric invariant bilinear form, p is a finite dimensional complex super vector space with a nondegenerate supersymmetric bilinear form, and ν : r → osp(p) is a homomorphism of Lie superalgebras.In this paper, we give a necessary and sufficient condition for r ⊕ p to be a quadratic Lie superalgebra.Then, we define the cubic Dirac operator D(g, r) on g and give a formula of(D(g, r))~2. Finally, we get the Vogan's conjecture for quadratic Lie superalgebras by D(g, r).

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.

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.

5.

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,

6.

Derivations and extensions of lie color algebra





张庆成 张永正《数学物理学报(B辑英文版)》,2008年第28卷第4期


In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.

7.

SUPERSYMMETRIC INVARIANCE AND UNIVERSAL CENTRAL EXTENSIONS OF LIE SUPERTRIPLE SYSTEMS





张庆成 魏竹 褚颖娜 张永平《数学物理学报(B辑英文版)》,2014年第2期


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.

8.

Cartan Invariants in the Category of Restricted Representation for gl（m｜n）





Li Sun ZHENG ;Bin SHU《数学学报(英文版)》,2014年第30卷第5期


Let k be an algebraically closed field of characteristic p 〉 2, and gl（m｜n） be the general linear Lie superalgebra over k. The Cartan invariants for the restricted supermodule category for gl（m｜n） are presented.

9.

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…

10.

N = 4 Supersymmetric Morse Oscillator and Its SpectrumGenerating Algebra





RUAN Dong SUN HongZhou《理论物理通讯》,2005年第44卷第3期


In this paper N = 4 supersymmetry of generalized Morse oscillators in one dimension is studied. Both bound states and scattering states of its four superpartner Hamiltonians are analyzed by using unitary irreducible representations of the noncompact Lie algebra su（1,1）. The spectrumgenerating algebra governing the Hamiltonian of the N = 4 supersymmetric Morse oscillator is shown to be connected with the realization of Lie superalgebra osp（1,2） or B（0,1） in terms of the variables of a supersymmetric twodimensional harmonic oscillator.

11.

Finite Symmetry Transformation Groups and Exact Solutions of Lax Integrable Systems





MA HongCai LOU SenYue《理论物理通讯》,2005年第44卷第2期


The general Lie point symmetry groups of the NizhnikNovikovVesselov （NNV） equation and the asymmetric NNV equation are given by a simple direct method with help of their weak Lax pairs.

12.

RESEARCH ANNOUNCEMENTS Structure of Solvable Quadratic Lie Algebras





朱林生《数学进展》,2005年第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. Besides semisimple Lie algebras, interesting quadratic Lie algebras include the KacMoody algebras and the Extended Affine Lie algebras.

13.

sl（1｜2） SuperToda Fields





YANG ZhanYing ;XUE PanPan ;ZHAO Liu ;SHI KangJie《理论物理通讯》,2008年第50卷第11期


Explicit exact solution of supersymmetric Toda fields associated with the Lie superalgebra s/（2｜ 1） is constructed. The approach used is a super extension of LeznovSaveliev algebraic analysis, which is based on a pair of chiral and antichiral DrienfeldSokolov systems. Though such approach is well understood for Toda field theories associated with ordinary Lie algebras, its super analogue was only successful in the super Liouville case with the underlying Lie superalgebra osp（1｜2）. The problem lies in that a key step in the construction makes use of the tensor product decom position of the highest weight representations of the underlying Lie superalgebra, which is not clear until recently. So our construction made in this paper presents a first explicit example of LeznovSaveliev analysis for super Toda systems associated with underlying Lie superalgebras of the rank higher than 1.

14.

A class of generalized odd Hamiltonian Lie superalgebras





Li Ren Qiang Mu Yongzheng Zhang《Frontiers of Mathematics in China》,2014年第9卷第5期


We study class of finitedimensional Cantantype Lie superalgebras HO（m） over a field of prime characteristic, which can be regarded as extensions of odd Hamiltonian superalgebra HO. And we also determine the derivation superalgebras of Lie superalgebras HO（m）.

15.

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.

16.

The Frattini Subalgebra of Restricted Lie Superalgebras 被引次数：6





Liang Yun CHEN Dao Ji MENG Yong Zheng ZHANG《数学学报(英文版)》,2006年第22卷第5期


In the present paper, we study the Frattini subalgebra of a restricted Lie superalgebra （L, [p]）. We show first that if L = A1 ＋ A2 ＋… ＋An, then Фp（L） = Фp（A1） ＋Фp（A2） ＋…＋Фp（An）, where each Ai is a pideal of L. We then obtain two results： F（L） = Ф（L） = J（L） = L if and only if L is nilpotent; Fp（L） and F（L） are nilpotent ideals of L if L is solvable. In addition, necessary and sufficient conditions are found for Фpfree restricted Lie superalgebras. Finally, we discuss the relationships of Eprestricted Lie superalgebras and Erestricted Lie superalgebras.

17.

Peaked Traveling Wave Solutions to a Generalized Novikov Equation with Cubic and Quadratic Nonlinearities





李国芹 屈长征《理论物理通讯》,2014年第6期


The CamassaHolm equation, DegasperisProcesi equation and Novikov equation are the three typical integrable evolution equations admitting peaked solitons. In this paper, a generalized Novikov equation with cubic and quadratic nonlinearities is studied, which is regarded as a generalization of these three wellknown studied equations. It is shown that this equation admits single peaked traveling wave solutions, periodic peaked traveling wave solutions, and multipeaked traveling wave solutions.

18.

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35卷第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).

19.

NonLie Symmetry Groups of （2＋1）Dimensional Nonlinear Systems





MA HongCai LOU SenYue《理论物理通讯》,2006年第46卷第6期


A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Applying the modified direct method to the wellknown （2＋1）dimensional asymmetric NizhnikNovikovVesselov equation and Nizhnik NovikovVesselov equation, both the Lie point symmetry groups and the nonLie symmetry groups are obtained. The Lie symmetry groups obtained via traditional Lie approaches are only speciai cases. Furthermore, the expressions of the exact finite transformations of the Lie groups are much simpler than those obtained via the standard approaches.

20.

B(0,N)graded Lie superalgebras coordinatized by quantum tori Dedicated to Professor Sheng GONG on the occasion of his 75th birthday





CHEN Hongjia GAO Yun & SHANG Shikui Department of Mathematics University of Science and Technology of China Hefei 230026 China Department of Mathematics and Statistics York University Toronto Ontario Canada M3J 1P3《中国科学A辑(英文版)》,2006年第11期


We use a fermionic extension of the bosonic module to obtain a class of B(0, A)graded Lie superalgebras with nontrivial central extensions.
