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Special odd lie superalgebras in prime characteristic

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Science China Mathematics 2012年第3期55卷 567-576页

作者： LIU WenDe YUAN JiXia Department of Mathematics Harbin Institute of Technology Harbin 150006 China School of Mathematical Sciences Harbin Normal University Harbin 150025 China

Let g be a finite dimensional special odd lie superalgebra over an algebraically closed field F of characteristic p > *** sufficient and necessary condition is given for g possessing a nondegenerate associative form a... 详细信息

关键词： lie superalgebra associative form cohomology

Embedding theorem of Z-graded lie superalgebras

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Science China Mathematics 1998年第10期41卷 1009-1016页

作者：张永正沈光宇

The embedding theorem ofZ-graded lie superalgebras is given and proved. As a subsidiary result it is proved that a transitiveZ-graded restricted lie superalgebm $G = \mathop \oplus \limits_{i \geqslant - 1} G_i $ must... 详细信息

关键词： lie superalgebra tensor algebra exterior algebra dlvided power algebra coalgebra restricted lie superalgebra

Left-supersymmetric-Structures onlie superalgebras

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Communications in Mathematical Research 1999年第2期 83-90页

作者： Wang Xiandong (Department of Applied Mathematics, Xidian University, Xi’an, 710071)

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙ，ｔｈｅｓｔｕｄｙｏｆｌｅｆｔ－ｓｙｍｍｅｔｒｉｃａｌｇｅｂｒａｓａｎｄｌｅｆｔ－ｓｙｍｍｅｔｒｉｃｓｔｒｕｃｔｕｒｅｓｏｎＬｉｅａｌｇｅｂｒａｓｈａｓｂｅｃｏｍｅａｎｉ... 详细信息

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙ，ｔｈｅｓｔｕｄｙｏｆｌｅｆｔ－ｓｙｍｍｅｔｒｉｃａｌｇｅｂｒａｓａｎｄｌｅｆｔ－ｓｙｍｍｅｔｒｉｃｓｔｒｕｃｔｕｒｅｓｏｎＬｉｅａｌｇｅｂｒａｓｈａｓｂｅｃｏｍｅａｎｉｎｔｅｒｅｓｔｉｎｇｓｕｂｊｅｃｔ...

关键词： lie superalgebra Left supersymmetric Algebra Left supersymmetric Structure

The super-classical-Boussinesq hierarchy and its super-Hamiltonian structure

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Chinese Physics B 2010年第7期19卷 23-27页

作者：陶司兴夏铁成 Department of Mathematics Shanghai University Department of Mathematics Shangqiu Normal University

Based on the constructed lie superalgebra, the super-classical-Boussinesq hierarchy is obtained. Then, its super- Hamiltonian structure is obtained by making use of super=trace identity. Furthermore, the super-classic... 详细信息

关键词： lie superalgebra super-trace identity super-integrable system super-Hamiltonian structure

Nonlinear Super Integrable Couplings of Super Dirac Hierarchy and Its Super Hamiltonian Structures

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Communications in Theoretical Physics 2012年第6期57卷 961-966页

作者：尤福财 Department of Basic Sciences Shenyang Institute of Engineering

We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix lie *** its super Hamiltonian structure is furnished by super trace *** its reduction,we gain the n... 详细信息

关键词： lie superalgebra nonlinear super integrable couplings super Dirac hierarchy super Hamiltonian structures

Filtration, automorphisms, and classification of infinite-dimensional odd contact superalgebras

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Frontiers of Mathematics in China 2013年第1期8卷 203-216页

作者： Jixia YUAN Wende LIU School of Mathematical Sciences HeilonKiiang University Harbin 150080 China School of Mathematical Sciences Harbin Normal University Harbin 150025 China

The principal filtration of the infinite-dimensional odd contact lie superalgebra over a field of characteristic p 〉 2 is proved to be invariant under the automorphism group by investigating ad-nilpotent elements and determining certain invariants such as subalgebras generated by some ad-nilpotent elements. Then, it is proved that two automorphisms coincide if and only if they coincide on the -1 component with respect to the principal grading. Finally, all the odd contact superalgebras are classified up to isomorphisms.

关键词： lie superalgebra filtration automorphism classification

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

On the Cohomology of Associative superalgebras

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Northeastern Mathematical Journal 2001年第2期17卷 175-180页

作者：王颖姚光同 Department of Mathematics Harbin Institute of Technology Harbin 150001 Department of Mathematics Keshan Teachers College Qiqihar Heilongjiang 161601

This paper presents a sufficient condition for the cohomology groups of an associative superalgebra to vanish. As its application, we prove that the cohomology groups H n(L,M) vanish when L is a strongly semi... 详细信息

关键词： cohomology associative superalgebra lie superalgebra

NEW SUPER-HAMILTONIAN STRUCTURES OF SUPER-DIRAC HIERARCHY

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Annals of Differential Equations 2012年第2期28卷 164-169页

作者： Yong Fang1,2,3, Yijun Hou1,2 , Huanhe Dong4, Jianhai Xue5 (1. Institute of Oceanology, Chinese Academy of Science, Qingdao 266071, Shandong 2. Key Laboratory of Ocean Circulation and Waves, Chinese Academy of Science, Qingdao 266071 3. Graduate University of Chinese Academy of Science, Beijing 100039 4. Information School, Shandong University of Science and Technology, Qingdao 266510 5. Thermoelectric Gas Company in Qingdao Development Zone, Qingdao 266555)

In this paper, we introduce the supertrace identity and its applications. A new eight-dimensional lie superalgebra is constructed and the super-Dirac hierarchy is derived. By the supertrace identity, we obtain the sup... 详细信息

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