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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

Left-Symmetric superalgebra Structures on an Infinite-Dimensional lie superalgebra

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Algebra Colloquium 2023年第3期30卷 429-438页

作者： Hongjia Chen Omer Hassan School of Mathematical Sciences University of Science and Technology of China Hefei 230026China

In this note, the compatible left-symmetric superalgebra structures on an infinite-dimensional lie superalgebra with some natural grading conditions are completely determined. The results of earlier work on left-symme... 详细信息

关键词： left-symmetric superalgebra Virasoro algebra lie superalgebra

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

The Derivation Algebra of the Cartan-type lie superalgebra H

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Chinese Quarterly Journal of Mathematics 2008年第3期23卷 409-414页

作者： CHEN Yu-zhen WANG Ying MA Bao-lin Department of Mathematics Henan Institute of Science and Technology Xinxiang 453003 China Department of Applied Mathematics Dalian University of Technology Dalian 116024 China

In this paper, the derivation algebra of lie superalgebra H of Caftan-type over F are determined by the calculating method in the situations of CharF = p ≥ 3 or m ≥ 2 or n ≥ 1. The main result is following： DerFH ... 详细信息

关键词： lie superalgebra derivation algebra

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

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

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Acta Mathematica Sinica,English Series 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

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 130024 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

ON SOLVABLE COMPLETE lie superalgebraS

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Chinese Annals of Mathematics,Series B 2003年第1期24卷 111-114页

作者： WANG LIYUN MENG DAOJI Department of Mathematics Shanghai Jiaotong University Shnaghai 200030 China.Department of Mathematics Nankai University Tianjin 300071 China.

The authors discuss the properties of solvable complete lie superalgebra, proving that solvable lie superalgebras of maximal rank are complete.

关键词： lie superalgebra Complete lie superalgebra Root space decomposition Solvable lie superalgebra Nilpotent lie superalgebra