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A New lie algebra and a Way to Generate Multiple Integrable Couplings

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Communications in Theoretical Physics 2007年第12期48卷 979-982页

作者： FENG Bin-Lu~(1,2)and HAN Bo~1~1 Department of Mathematics,Harbin Institute of Technology,Harbin 150001,China~2 Department of Mathematics,Weifang University,Weifang 261000,China Department of Mathematics Harbin Institute of Technology Harbin 150001 China Department of Mathematics Weifang University Weifang 261000 China

A new higher-dimensional lie algebra is constructed,which is used to generate multiple integrable couplingssimultaneously.From this,we come to a general approach for seeking multi-integrable couplings of the known int... 详细信息

关键词： lie algebra integrable hierarchy Hamiltonian structure

The q-Analog Klein Bottle lie algebra

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algebra Colloquium 2014年第4期21卷 561-574页

作者： Cuipo Jiang Jingjing Jiang Yufeng Pei Department of Mathematics Shanghai diaotong UniversityShanghai 200240 China Department of Mathematics Shanghai Normal University Shanghai 200234 China

In this paper, we study an infinite-dimensional lie algebra Bq, called the q-analog Klein bottle lie algebra. We show that Bq is a finitely generated simple lie algebra with a unique （up to scalars） symmetric invari... 详细信息

关键词： lie algebra Klein bottle invariant bilinear form central extension derivation

lie symmetry algebra of one-dimensional nonconservative dynamical systems

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Chinese Physics B 2007年第9期16卷 2665-2670页

作者：刘翠梅吴润衡傅景礼 Institute of Mathematical Physics Zhejiang Sci-Tech University Hangzhou 310018 China Department of Physics Shangqiu Teachers College Shangqiu 476000 China Department of Mathematics Beijing Industrial University Beijing 100080 China Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China)

lie symmetry algebra of linear nonconservative dynamical systems is studied in this paper. By using 1-1 mapping, the lie point and lie contact symmetry algebras are obtained from two independent solutions of the one-d... 详细信息

关键词： lie algebra symmetry infinitesimal transformation nonconserved dynamical system

NEW SET OF SYMMETRIES FOR THE INTEGRABLE EQUATIONS, lie algebra, NON-ISOSPECTRAL EVOLUTION EQUATIONS (Ⅲ)

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Science Bulletin 1986年第5期 289-294页

作者：朱国城李翊神 University of Science and Technology of China Department of Mathematics Hefei

In this note we give two sets of symmetries for the nonlinear evolution equations related to the Kaup-Newell eigenvalue problem and propose an infinite dimensional lie algebra for them.

关键词： NON-ISOSPECTRAL EVOLUTION EQUATIONS lie algebra NEW SET OF SYMMETRIES FOR THE INTEGRABLE EQUATIONS

THE lie algebra ADMITTED BY ANORDINARY DIFFERENTIAL EQUATION SYSTEM

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Annals of Differential Equations 1998年第2期14卷 33-44页

作者：管克英刘胜雷锦志北京航空航天大学

The lie algebra, which is generated by all generators of one parameter lie groups admitted locally by a given ordinary differential equation system, is proved to be of finite rank and with useful structure in the study of integrating the system. This result is more flexible than the traditional lie group theory of ordinary differential equation.

关键词： lie algebra module basis first integral

lie algebras Associated with Group U(n)

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Communications in Theoretical Physics 2007年第8期48卷 215-226页

作者： Honwah Tam Department of Computer Science Hong Kong Baptist UniversityHong KongChina

Starting from the subgroups of the group U（n）,the corresponding lie algebras of the lie algebra A;arepresented,from which two well-known simple equivalent matrix lie algebras are given.It follows that a few expandinglie algebras are obtained by enlarging matrices.Some of them can be devoted to producing double integrable couplingsof the soliton hierarchies of nonlinear evolution equations.Others can be used to generate integrable oouplings involvingmore potential functions.The above lie algebras are classified into two types.Only one type can generate the integrablecouplings,whose Hamiltonian structure could be obtained by use of the quadratic-form identity.In addition,onecondition on searching for integrable couplings is improved such that more useful lie algebras are enlightened to engender.Then two explicit examples are shown to illustrate the applications of the lie algebras.Finally,with the help of closedcycling operation relations,another way of producing higher-dimensional lie algebras is given.

关键词： lie algebra group integrable couplings

Generalised Chain Conditions,Prime Ideals,and Classes of Locally Finite lie algebras

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algebra Colloquium 2021年第1期28卷 63-86页

作者： Falih A.M.Aldosray Ian Stewart Department of Mathematics Umm Al-Qura UniversityP.O.Box 56199MakkahSaudi Arabia Mathematics Institute University of WarwickCoventry CV47ALUK

A Noetherian(Artinian)lie algebra satisfies the maximal(minimal)condition for ideals.Generalisations include quasi-Noetherian and quasi-Artinian lie algebras.We study conditions on prime ideals relating these properties.We prove that the radical of any ideal of a quasi-Artinian lie algebra is the intersection of finitely many prime ideals,and an ideally finite lie algebra is quasi-Noetherian if and only if it is quasi-Artinian.Both properties are equivalent to soluble-by-finite.We also prove a structure theorem for serially finite Artinian lie algebras.

关键词： lie algebra chain condition prime ideal radical locally finite

Global weak solutions to Landau-Lifshitz equations into compact lie algebras

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Frontiers of Mathematics in China 2019年第6期14卷 1163-1196页

作者： Zonglin JIA Youde WANG Institute of Applied Physics and Computational Mathematics China Academy of Engineering PhysicsBeijing 100088China College of Mathematics and Information Sciences Guangzhou UniversityGuangzhou 510006China Hua Loo-Keng Key Laboratory of Mathematics Institute of MathematicsAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

We consider a parabolic system from a bounded domain in a Euclidean space or a closed Riernannian manifold into a unit sphere in a compact lie algebra g,which can be viewed as the extension of Landau-Lifshitz(LL)equation and was proposed by V.Arnold.We follow the ideas taken from the work by the second author to show the existence of global weak solutions to the Cauchy problems of such LL equations from an n-dimensional closed Riernannian manifold T or a bounded domain in R^n into a unit sphere Sg(1)in g.In particular,we consider the Hamiltonian system associated with the nonlocal energy micromagnetic energy defined on a bounded domain of R^31 and show the initial-boundary value problem to such LL equation without damping terms admits a global weak solution.The key ingredient of this article consists of the choices of test functions and approximate equations.

关键词： Landau-Lifshitz(LL)equations lie algebra test functions

Cohomology of the Universal Enveloping algebras of Certain Bigraded lie algebras

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Acta Mathematica Sinica,English Series 2018年第10期34卷 1611-1625页

作者： Li Nan ZHONG Hao ZHAO Wen Huai SHEN School of Mathematical Sciences South China Normal University Guangzhou 510631 P. R. China Department of Mathematics Yanbian University Yanji 133000 P. R. China

Let p be an odd prime and q = 2（p- 1）. Up to total degree t - s 〈 max（（5p^3 ＋ 6p^2 ＋6p ＋4）q- 10,p^4q}, the generators of H^s,t（U（L））, the cohomology of the universal enveloping algebra of a bigraded lie algebra L, are determined and their convergence is also verified. Furthermore our results reveal that this cohomology satisfies an analogous Poindare duality property. This largely generalizes an earlier classical results due to J. P. May.

关键词： Steenrod algebra Hopf algebra lie algebra spectral sequence stable homotopy groups of sphere