The symmetries of a （2＋1）-dimensional shallow water wave system, which is newly constructed through applying variation principle of analytic mechanics, are researched in this paper. The Lie symmetries and the corre...The symmetries of a （2＋1）-dimensional shallow water wave system, which is newly constructed through applying variation principle of analytic mechanics, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. The （1＋1） dimensional displacement shallow water wave equation can be derived from the reductions when special symmetry parameters are chosen.展开更多
In a recent article by Liu,Pei,and Zhu,Lie bialgebra structures on the twisted Heisenberg-Virasoro algebra were determined. By disposing the indexing set, the generalized Heisenberg-Virasoro algebra was considered. It...In a recent article by Liu,Pei,and Zhu,Lie bialgebra structures on the twisted Heisenberg-Virasoro algebra were determined. By disposing the indexing set, the generalized Heisenberg-Virasoro algebra was considered. It is proved that all Lie bialgebra structures on centerless generalized Heisenberg-Virasoro algebra L are coboundary triangular by proving that the first cohomology group H1 (L,V) =0.展开更多
A bilinear form f on a nonassociative triple system T is said to be invariant if and only if f( abc ,d) = f(a, dcb ) = f(c, bad ) for all a,b,c,d ∈ T . (T ,f) is called a pseudo-metric triple system if f is non-degen...A bilinear form f on a nonassociative triple system T is said to be invariant if and only if f( abc ,d) = f(a, dcb ) = f(c, bad ) for all a,b,c,d ∈ T . (T ,f) is called a pseudo-metric triple system if f is non-degenerate and invariant. A decomposition theory for triple systems and pseudo-metric triple systems is established. Moreover, the ?nite-dimensional metric Lie triple systems are characterized in terms of the structure of the non-degenerate, invariant and symmetric bilinear forms on them.展开更多
基金supported by National Natural Science Foundation of China under Grant Nos.10475055 and 90503006
文摘The symmetries of a （2＋1）-dimensional shallow water wave system, which is newly constructed through applying variation principle of analytic mechanics, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. The （1＋1） dimensional displacement shallow water wave equation can be derived from the reductions when special symmetry parameters are chosen.
基金National Natural Science Foundations of China(No.11001046,No.11201305)the Fundamental Research Funds for the Central Universities+1 种基金Foundation of Outstanding Young Teachers of Donghua University,ChinaInnovation Project of Shanghai Education Committee,China(No.12YZ081)
文摘In a recent article by Liu,Pei,and Zhu,Lie bialgebra structures on the twisted Heisenberg-Virasoro algebra were determined. By disposing the indexing set, the generalized Heisenberg-Virasoro algebra was considered. It is proved that all Lie bialgebra structures on centerless generalized Heisenberg-Virasoro algebra L are coboundary triangular by proving that the first cohomology group H1 (L,V) =0.
文摘A bilinear form f on a nonassociative triple system T is said to be invariant if and only if f( abc ,d) = f(a, dcb ) = f(c, bad ) for all a,b,c,d ∈ T . (T ,f) is called a pseudo-metric triple system if f is non-degenerate and invariant. A decomposition theory for triple systems and pseudo-metric triple systems is established. Moreover, the ?nite-dimensional metric Lie triple systems are characterized in terms of the structure of the non-degenerate, invariant and symmetric bilinear forms on them.
