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A new eight-dimensional lie superalgebra and two corresponding hierarchies of evolution equations

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Chinese Physics B 2010年第1期19卷 7-12页

作者：王新赠董焕河 College of Information Science and Engineering Shandong University of Science and Technology

A new eight-dimensional lie superalgebra is constructed and two isospectral problems with six potentials are designed. Corresponding hierarchies of nonlinear evolution equations, as well as super-AKNS and super-Levi, are derived. Their super-Hamiltonian structures are established by making use of the supertrace identity, and they are integrable in the sense of Liouville.

关键词： lie superalgebra supertrace identity superintegrable system super-Hamiltonian structure

Irreducible Wakimoto-like Modules for the lie superalgebra D(2,1;α)

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Acta Mathematica Sinica,English Series 2018年第10期34卷 1578-1588页

作者： Jin CHENG Zi Ting ZENG School of Mathematics and Statistics Shandong Normal University Ji'nan 250014 P. R. China School of Mathematical Science Beijing Normal University Beijing 100875 P. R. China

By using the idea of Wakimoto＇s free field, we construct a class of representations for the lie superalgebra D（2, 1; α） on the tensor product of a polynomial algebra and an exterior algebra involving one parameter A. Then we obtain the necessary and sufficient condition for the representations to be irreducible. In fact. the representation is irreducible if and only if the parameter ,λ satisfies （λ＋m）（λ-1＋α/αm）≠0 for any m∈Z＋.

关键词： lie superalgebra representation Wakimoto's free field

COHERENT STATE REPRESENTATION OF THE lie superalgebra OSP(1,2)

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Acta Mathematica Scientia 1996年第S1期16卷 34-45页

作者：曾高坚匡乐满 CCAST (World Laboratory) P.O.Box 8730 Beijing 100080 China

We construct coherent states associated with the lie superalgebra OSP(1. 2) with the aid of two SU(2) coherent states and discuss their properties in detail. We also evaluate the matrix elements of the OSP(1, 2) generators in the coherent-state representation and give a realization for the OSP(1, 2) generators in the coherent state space.

关键词： Coherent state lie superalgebra

Super-biderivations and Post-lie superalgebras on Some lie superalgebras

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数学学报:英文版 2023年第9期39卷 1736-1754页

作者： Munayim Dilxat Shou Lan Gao Dong Liu College of Mathematics and System Sciences Xinjiang UniversityUrumqi830046P.R.China Department of Mathematics Huzhou UniversityHuzhou313000P.R.China

In this paper,all symmetric super-biderivations of some lie superalgebras are *** an application,commutative post-lie super algebra structures on these lie super algebras are also obtained.

关键词： lie superalgebra super-biderivation post-lie superalgebra

Super-biderivations of not-finitely graded lie superalgebras related to generalized super-Virasoro algebras

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Frontiers of Mathematics in China 2020年第6期15卷 1295-1306页

作者： Zhuo ZHANG Jixia YUAN Xiaomin TANG School of Mathematical Sciences Heilongjiang UniversityHarbin 150080China

We mainly study the super-biderivations of not-finitely graded lie superalgebras related to generalized super-Virasoro *** particular,we prove that all super-biderivations of not-finitely graded lie superalgebras rela... 详细信息

关键词： lie superalgebra super-Virasoro algebras super-biderivation inner super-biderivations

Z-Graded lie superalgebras with Depth One over Fields of Prime Characteristic

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Acta Mathematica Sinica,English Series 2002年第4期18卷 687-700页

作者： Yong Zheng ZHANG Department of Mathematics. Northeast Normal University. Changchun 130024. P. R. China Department of Mathematics Northeast Normal University Changchun P. R. China

Let F be a field of characteristic p>3, and L=_(i≥-1) L_i the finite-dimensional transitive Z-graded simple lie superalgebra over F. In this paper L is determined if the Z-graded lie superalgebra L_(-1) L_O is isomo... 详细信息

关键词： lie superalgebra Exterior algebra Field of prime characteristic

Grobner-Shirshov Bases for Exceptional lie superalgebras

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Algebra Colloquium 2015年第1期22卷 1-10页

作者： Dong-il Lee Department of Mathematics Seoul Women's University Seoul 139-774 Korea

For exceptional lie superalgebras D（2, 1; α）, G（3） and F（4）, GrSbner-Shirshov bases and the corresponding super-Lyndon-Shirshov monomial bases are constructed.

关键词： Grobner-Shirshov basis lie superalgebra super-Lyndon-Shirshov monomial

DERIVATION ALGEBRAS OF THE MODULAR lie superalgebraS W AND S OF CARTAN-TYPE

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Acta Mathematica Scientia 2000年第1期20卷 137-144页

作者：张庆成张永正 Department of Mathematics Jilin Vocational Teacher's College Changchun 130052 China Department of Mathematics Northeast Normal University Changchun 130024 China

Let F be a field and char F = p > 3. In this paper the derivation algebras of lie superalgebras W and S of Cartan-type over F are determined by the calculating method.

关键词： lie superalgebra exterior algebra derivation algebra

On the Structure of Quantum Toroidal superalgebraε_(m|n)

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Acta Mathematica Sinica,English Series 2023年第11期39卷 2117-2138页

作者： Xiang Hua WU Hong Da LIN Hong Lian ZHANG Department of Mathematics Shanghai UniversityShanghai 200444P.R.China Newtouch Center for Mathematics of Shanghai University Shanghai 200444P.R.China

Recently the quantum toroidal superalgebraε_(m|n)associated with gl_(m|n)was introduced by *** and ***,which is not a quantum Kac-Moody *** quantum toroidal superalgebraε_(m|n)exploits infinite sequences of generators and relations of the form,which are called Drinfeld *** this paper,we use only finite set of generators and relations to define an associative algebraε'_(m|n)and show that there exists an epimorphism fromε'_(m|n)to the quantum toroidal superalgebraε_(m|n).In particular,the structure ofε'_(m|n)enjoys some properties like Drinfeld-Jimbo realization.

关键词： Quantum toroidal superalgebra Drinfeld realization lie superalgebra