In this article, Lie super-bialgebra structures on generalized super-Virasoro algebras/： are considered. It is proved that all such Lie super-bialgebras are coboundary triangular Lie super-bialgebras if and only if H...In this article, Lie super-bialgebra structures on generalized super-Virasoro algebras/： are considered. It is proved that all such Lie super-bialgebras are coboundary triangular Lie super-bialgebras if and only if Hi（ ） = 0.展开更多
In this article, we prove that if B is a simple binary-Lie superalgebra whose even part is isomorphic to sl2(F) ?and whose odd part is a completely reducible binary-Lie-module over the even part, then B is a Lie super...In this article, we prove that if B is a simple binary-Lie superalgebra whose even part is isomorphic to sl2(F) ?and whose odd part is a completely reducible binary-Lie-module over the even part, then B is a Lie superalgebra. We introduce also a binary-Lie module over which is sl2(F) not completely reducible.展开更多
Based on the basis of the constructed Lie super algebra, the super-isospectral problem of KN hierarchy is considered. Under the frame of the zero curvature equation, the super-KN hierarchy is obtained. Furthermore, it...Based on the basis of the constructed Lie super algebra, the super-isospectral problem of KN hierarchy is considered. Under the frame of the zero curvature equation, the super-KN hierarchy is obtained. Furthermore, its super-Hamiltonian structure is presented by using super-trace identity and it has super-bi-Hamiltonian structure.展开更多
Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identi...Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identity, and the conserved functionals were proved to be in involution in pairs under the defined Poisson bracket. As its reduction,special cases of this nonlinear super integrable couplings were obtained.展开更多
Based upon the basis of Lie super algebra B(0,1), the super Tu equation hierarchy with self-con- sistent sources was presented. Furthermore, the infinite conservation laws of above hierarchy were given.
Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. And its super Hamiltonian structures were established by using super trace identit...Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. And its super Hamiltonian structures were established by using super trace identity. As its reduction, special cases of this nonlinear super integrable coupling were obtained.展开更多
Nonlinear super integrable couplings of the super Yang hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identity. ...Nonlinear super integrable couplings of the super Yang hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identity. As its reduction, nonlinear integrable couplings of Yang hierarchy were obtained.展开更多
This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra A^-M. By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which ...This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra A^-M. By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which possesses the Hamiltonian structure. As its reduction cases, the multicomponent （2＋1）-dimensional Glachette-Johnson （G J） hierarchy is given. Finally, the super-integrable coupling system of multicomponent （2＋1）-dimensional GJ hierarchy is established through enlarging the spectral problem.展开更多
We consider the simple restricted modules for special contact Lie superalgebras of odd type over an algebraically closed field of characteristic p>3.We give a sufficient and necessary condition in terms of typical ...We consider the simple restricted modules for special contact Lie superalgebras of odd type over an algebraically closed field of characteristic p>3.We give a sufficient and necessary condition in terms of typical or atypical weights for restricted Kac modules to be simple.In the process,we also determine the socle for each restricted Kac module and the length for each simple restricted module.展开更多
In this paper we give the definition of super hyperbolic type Kac-MoodyLie algebra and discuss its imaginary roots systems. Finally, we give the necessary andsufficient condition for Cartan matrices to be of super hyp...In this paper we give the definition of super hyperbolic type Kac-MoodyLie algebra and discuss its imaginary roots systems. Finally, we give the necessary andsufficient condition for Cartan matrices to be of super hyperbolic type.展开更多
基金Supported by the Foundation of Shanghai Education Committee (06FZ029)NSF of China (10471091)"One Hundred Program" from University of Science and Technology of China
文摘In this article, Lie super-bialgebra structures on generalized super-Virasoro algebras/： are considered. It is proved that all such Lie super-bialgebras are coboundary triangular Lie super-bialgebras if and only if Hi（ ） = 0.
文摘In this article, we prove that if B is a simple binary-Lie superalgebra whose even part is isomorphic to sl2(F) ?and whose odd part is a completely reducible binary-Lie-module over the even part, then B is a Lie superalgebra. We introduce also a binary-Lie module over which is sl2(F) not completely reducible.
基金＊Supported by the Natural Science Foundation of China under Grant Nos. 61072147, 11071159, the Natural Science Foundation of Shanghai urlder Grant No. 09ZR1410800, the Shanghai Leading Academic Discipline Project under Grant No. J50101, and the National Key Basic Research Project of China under Grant No. KLMM0806
文摘Based on the basis of the constructed Lie super algebra, the super-isospectral problem of KN hierarchy is considered. Under the frame of the zero curvature equation, the super-KN hierarchy is obtained. Furthermore, its super-Hamiltonian structure is presented by using super-trace identity and it has super-bi-Hamiltonian structure.
基金ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China （No.61072147）, the Natural Science Foundation of Henan Province （No.132300410202）, the Science and Technology Key Research Foundation of the Education DeparuHent of Henan Province （No. 12A 110017） and the Youth Research Foundation of Shangqiu Normal University （No. 2011QN12）.
基金Supported by the Natural Science Foundation of Henan Province（162300410075） the Science and Technology Key Research Foundation of the Education Department of Henan Province（14A110010） the Youth Backbone Teacher Foundationof Shangqiu Normal University（2013GGJS02）
文摘Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identity, and the conserved functionals were proved to be in involution in pairs under the defined Poisson bracket. As its reduction,special cases of this nonlinear super integrable couplings were obtained.
文摘Based upon the basis of Lie super algebra B(0,1), the super Tu equation hierarchy with self-con- sistent sources was presented. Furthermore, the infinite conservation laws of above hierarchy were given.
文摘Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. And its super Hamiltonian structures were established by using super trace identity. As its reduction, special cases of this nonlinear super integrable coupling were obtained.
文摘Nonlinear super integrable couplings of the super Yang hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identity. As its reduction, nonlinear integrable couplings of Yang hierarchy were obtained.
基金supported by the National Key Basic Research Development of China (Grant No 2004CB318000)
文摘This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra A^-M. By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which possesses the Hamiltonian structure. As its reduction cases, the multicomponent （2＋1）-dimensional Glachette-Johnson （G J） hierarchy is given. Finally, the super-integrable coupling system of multicomponent （2＋1）-dimensional GJ hierarchy is established through enlarging the spectral problem.
基金supported in part by the National Natural Science Foundation of China(Grant No.11701158).
文摘We consider the simple restricted modules for special contact Lie superalgebras of odd type over an algebraically closed field of characteristic p>3.We give a sufficient and necessary condition in terms of typical or atypical weights for restricted Kac modules to be simple.In the process,we also determine the socle for each restricted Kac module and the length for each simple restricted module.
文摘In this paper we give the definition of super hyperbolic type Kac-MoodyLie algebra and discuss its imaginary roots systems. Finally, we give the necessary andsufficient condition for Cartan matrices to be of super hyperbolic type.
