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1.
两个高维loop代数及应用 总被引:5,自引:1,他引:4
借助于循环数,构造了维数分别是5(s+1)和4(s+1)的两个高维loop代数.为了计算方便,本文只考虑s=1时的应用.利用第一个loop代数■_1~*得到了具有4-Hamilton结构的一个广义AKNS族,该方程族可约化为著名的AKNS族.利用第二个loop代数■_2~*,得到了具有4个分量位势函数的4-Hamilton结构方程族,该族可约化为一个非线性耦合Burgers方程和一个耦合的KdV方程. 相似文献
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赵晶 《数学的实践与认识》2007,37(8):61-65
构造了一类3×3的反对称loop代数,由此设计了一个含5个位势函数的等谱问题;利用屠格式导出了一个Liouville可积系统,且拥有双Hamilton结构. 相似文献
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基于sl(4,(C))的loop代数的非平凡李代数分裂,构造了5类新的孤子方程族.这些代数分裂通过构造从正李子代数到负李子代数的线性箅子B统一得到.对所有可能的线性箅子B进行分类,证明存在5类4×4仿射B-型KdV方程族.利用Adler- Konstant- Symes理论获得了这些方程族的Hamilton结构,并利用loop群方法得到其B(a)cklund变换. 相似文献
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利用一个广义等谱问题的相容性得到了一个广义零曲率方程.作为其应用,首先利用loop代数设计了两个广义等谱问题,然后利用零曲率方程导出了两类(2+1)维Lax可积系统. 相似文献
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本文利用已有的loop代数$\widetilde{A}_{1}$构造出代数系统$X$,然后建立了一个新的等谱问题得到著名的Volterra lattice可积系,最后通过构造出的$X$的扩展代数系统$\widetilde{X}$得到已有的可积系的可积耦合系统. 相似文献
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两类新的loop代数及其应用 总被引:1,自引:0,他引:1
利用构造的两类特殊 loop代数 ,建立了线性等谱问题 .作为应用 ,求得了著名的 Kd V方程族和 Tu方程族的可积耦合系统 .这种方法可以普遍地应用 相似文献
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We study conformal biderivations of a Lie conformal algebra. First, we give the definition of a conformal biderivation. Next, we determine the conformal biderivations of loop W(a, b) Lie conformal algebra, loop Virasoro Lie conformal algebra, and Virasoro Lie conformal algebra. Especially, all conformal biderivations on Virasoro Lie conformal algebra are inner conformal biderivations. 相似文献
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Yongxin Zhou 《代数通讯》2013,41(1):523-539
In this paper we establish a relationship between alternative loop algebras and Cayley-Dickson algebras: any Cayley-Dickson algebra is a quotient algebra of an alternative loop algebra. Thus we give a new way of representing a Cayley-Dickson algebra. As an application, a result of Luiz G. X. de Barros is generalized. 相似文献
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In this paper we first present a 3-dimensional Lie algebra H and enlarge it into a 6-dimensional Lie algebra T with corresponding loop algebras?H and?T, respectively. By using the loop algebra?H and the Tu scheme, we obtain an integrable hierarchy from which we derive a new Darboux transformation to produce a set of exact periodic solutions. With the loop algebra?T, a new integrable-coupling hierarchy is obtained and reduced to some variable-coefficient nonlinear equations, whose Hamiltonian structure is derived by using the variational identity. Furthermore, we construct a higher-dimensional loop algebraˉH of the Lie algebra H from which a new Liouville-integrable hierarchy with 5-potential functions is produced and reduced to a complex m Kd V equation, whose 3-Hamiltonian structure can be obtained by using the trace identity. A new approach is then given for deriving multiHamiltonian structures of integrable hierarchies. Finally, we extend the loop algebra?H to obtain an integrable hierarchy with variable coefficients. 相似文献
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《Chaos, solitons, and fractals》2005,23(2):651-655
Construction of a type of simple loop algebra is devoted to establishing an isospectral problem. It follows that the multi-component KdV hierarchy of soliton equations is obtained. Further, an expanded loop algebra of the above algebra is presented, which is used to work out the multi-component integrable coupling system of the multi-component KdV hierarchy. 相似文献
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V. N. Zhelyabin 《Siberian Mathematical Journal》2009,50(6):1011-1026
Under study are the pointed unital coassociative cocommutative Moufang H-bialgebras. We prove an analog of the Cartier-Kostant-Milnor-Moore theorem for weakly associative Moufang H-bialgebras. If the primitive elements commute with group-like elements then these Moufang H-bialgebras are isomorphic to the tensor product of a universal enveloping algebra of a Malcev algebra and a loop algebra
constructed by a Moufang loop. 相似文献
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一个Lie代数的子代数及其相关的两类Loop代数 总被引:8,自引:0,他引:8
本文构造了Lie代数A2的一个子代数A2,通过选取恰当的基元阶数得到相应的一个loop代数A2,由此设计一个等谱问题,利用屠格式得到了一个新的Liouville可积的Hamilton方程族.作为其约化情形,得到了一个非线性有理分式型演化方程.再由一个矩阵变换,得到了换位运算与A2等价的Lie代数A1的一个子代数A1,将A1再扩展成一个新的高维loop代数G,利用G获得了所得方程族的一类扩展可积系统. 相似文献
18.
N. E. Dobrinskaya 《Proceedings of the Steklov Institute of Mathematics》2009,266(1):91-104
We consider a problem of calculating the loop space homology for so-called polyhedral products defined by an arbitrary simplicial
complex K. A presentation of this homology algebra is obtained from the homology of the complements of diagonal subspace arrangements,
which, in turn, is calculated using an infinite resolution of the exterior Stanley-Reisner algebra. We get an explicit presentation
of the loop homology algebra for polyhedral products for classes of simplicial complexes such as flag complexes and the duals
of sequentially Cohen-Macaulay complexes in terms of higher commutator products. We give a construction for the iteration
of higher products and discuss the relationship between this problem and problems in commutative algebra. 相似文献
19.
Tatsuro Ito 《代数通讯》2013,41(12):4557-4598
Recently Brian Hartwig and the second author found a presentation for the three-point 2 loop algebra by generators and relations. To obtain this presentation they defined a Lie algebra ? by generators and relations, and displayed an isomorphism from ? to the three-point 2 loop algebra. In this article, we describe the finite-dimensional irreducible ?-modules from multiple points of view. 相似文献
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Let F be an algebraically closed field of characteristic zero and L an RA loop. We prove that the loop algebra FL is in the variety generated by the split Cayley–Dickson algebra Z F over F. For RA2 loops of type M(Dih(A), ?1,g 0), we prove that the loop algebra is in the variety generated by the algebra 3 which is a noncommutative simple component of the loop algebra of a certain RA2 loop of order 16. The same does not hold for the RA2 loops of type M(G, ?1,g 0), where G is a non-Abelian group of exponent 4 having exactly 2 squares. 相似文献