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1.
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Hom-Gel'fand–Dorfman Super-bialgebras and Hom-Lie Conformal Superalgebras
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La Mei Yuan Sheng Chen Cai Xia He《数学学报(英文版)》,2017年第33卷第1期
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The aim of this paper is to introduce and study Hom-Gel'fand–Dorfman super-bialgebras and Hom-Lie conformal superalgebras. In this paper, we provide different ways for constructing HomGel'fand–Dorfman super-bialgebras. Also, we obtain some infinite-dimensional Hom-Lie superalgebras from affinization of Hom-Gel'fand–Dorfman super-bialgebras. Finally, we give a general construction of Hom-Lie conformal superalgebras from Hom-Lie superalgebras and establish the equivalence between quadratic Hom-Lie conformal superalgebras and Hom-Gel'fand–Dorfman super-bialgebras.
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2.
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Dirac Operators on Quadratic Lie Superalgebras
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《数学学报(英文版)》,2021年第8期
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Assume that r is a finite dimensional complex Lie superalgebra with a non-degenerate super-symmetric invariant bilinear form, p is a finite dimensional complex super vector space with a nondegenerate super-symmetric 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).
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3.
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超交换环上的一般线性李超代数的极大阶化子代数
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李杨 刘文德《数学研究及应用》,2015年第35卷第2期
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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.
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4.
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RESEARCH ANNOUNCEMENTS——Structure of Solvable Quadratic Lie Algebras
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朱林生《数学进展》,2005年第34卷第1期
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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 Kac-Moody 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 semi-simple 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.
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5.
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Omni-Lie superalgebras and Lie 2-superalgebras
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Tao Zhang Zhangju Liu《Frontiers of Mathematics in China》,2014年第9卷第5期
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We introduce the notion of omni-Lie superalgebras as a super version of an omni-Lie algebra introduced by Weinstein. This algebraic structure gives a nontrivial example of Leibniz superalgebras and Lie 2-superalgebras. We prove that there is a one-to-one correspondence between Dirac structures of the omni-Lie superalgebra and Lie superalgebra structures on a subspace of a super vector space,
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6.
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Derivations and extensions of lie color algebra
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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
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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.
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7.
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SUPERSYMMETRIC INVARIANCE AND UNIVERSAL CENTRAL EXTENSIONS OF LIE SUPERTRIPLE SYSTEMS
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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
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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.
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8.
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Cartan Invariants in the Category of Restricted Representation for gl（m｜n）
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Li Sun ZHENG ;Bin SHU《数学学报(英文版)》,2014年第30卷第5期
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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.
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9.
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EMBEDDING THEOREM OF FILTERED LIE SUPERALGEBRAS
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张永正 沈光宁《数学物理学报(B辑英文版)》,2001年第3期
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In recent years the Lie superalgebras have become a 8ubject of intere8t in both mathematicsand physic8[']--[41. We know that the embedding theorems of Z-graded Lie superalgebras andfiltered Lie superalgebras play an important role in the investigation of Lie superalgebras. Theembedding theorem of Z-greded 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…
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10.
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N = 4 Supersymmetric Morse Oscillator and Its Spectrum-Generating Algebra
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RUAN Dong SUN Hong-Zhou《理论物理通讯》,2005年第44卷第3期
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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 spectrum-generating 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 two-dimensional harmonic oscillator.
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11.
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Finite Symmetry Transformation Groups and Exact Solutions of Lax Integrable Systems
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MA Hong-Cai LOU Sen-Yue《理论物理通讯》,2005年第44卷第2期
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The general Lie point symmetry groups of the Nizhnik-Novikov-Vesselov （NNV） equation and the asymmetric NNV equation are given by a simple direct method with help of their weak Lax pairs.
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12.
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RESEARCH ANNOUNCEMENTS Structure of Solvable Quadratic Lie Algebras
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朱林生《数学进展》,2005年第1期
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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 Kac-Moody algebras and the Extended Affine Lie algebras.
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13.
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sl（1｜2） Super-Toda Fields
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YANG Zhan-Ying ;XUE Pan-Pan ;ZHAO Liu ;SHI Kang-Jie《理论物理通讯》,2008年第50卷第11期
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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 Leznov-Saveliev algebraic analysis, which is based on a pair of chiral and antichiral Drienfeld-Sokolov 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 Leznov-Saveliev analysis for super Toda systems associated with underlying Lie superalgebras of the rank higher than 1.
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14.
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A class of generalized odd Hamiltonian Lie superalgebras
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Li Ren Qiang Mu Yongzheng Zhang《Frontiers of Mathematics in China》,2014年第9卷第5期
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We study class of finite-dimensional Cantan-type 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）.
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15.
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关于完满的Lie超代数 被引次数：1
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张润萱 陈良云 张永正《东北数学》,2008年第24卷第6期
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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.
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16.
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The Frattini Subalgebra of Restricted Lie Superalgebras 被引次数：6
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Liang Yun CHEN Dao Ji MENG Yong Zheng ZHANG《数学学报(英文版)》,2006年第22卷第5期
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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 p-ideal 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 Фp-free restricted Lie superalgebras. Finally, we discuss the relationships of E-p-restricted Lie superalgebras and E-restricted Lie superalgebras.
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17.
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Peaked Traveling Wave Solutions to a Generalized Novikov Equation with Cubic and Quadratic Nonlinearities
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李国芹 屈长征《理论物理通讯》,2014年第6期
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The Camassa-Holm equation, Degasperis-Procesi 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 well-known studied equations. It is shown that this equation admits single peaked traveling wave solutions, periodic peaked traveling wave solutions, and multi-peaked traveling wave solutions.
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18.
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2-Local Automorphisms on Basic Classical Lie Superalgebras
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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
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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 non-degenerate invariant bilinear form and root space decomposition, we prove that every 2-local automorphism on G is an automorphism. Furthermore, we give an example of a 2-local automorphism which is not an automorphism on a subalgebra of Lie superalgebra spl(3, 3).
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19.
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Non-Lie Symmetry Groups of （2＋1）-Dimensional Nonlinear Systems
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MA Hong-Cai LOU Sen-Yue《理论物理通讯》,2006年第46卷第6期
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A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Applying the modified direct method to the well-known （2＋1）-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and Nizhnik Novikov-Vesselov equation, both the Lie point symmetry groups and the non-Lie 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.
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20.
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B(0,N)-graded Lie superalgebras coordinatized by quantum tori Dedicated to Professor Sheng GONG on the occasion of his 75th birthday
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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
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We use a fermionic extension of the bosonic module to obtain a class of B(0, A)graded Lie superalgebras with nontrivial central extensions.
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