We first prove that,for any generalized Hamiltonian type Lie algebra H,the first co- homology group H^1(H,H(?)H) is trivial.We then show that all Lie bialgebra structures on H are triangular.
In this paper, the dispersionless D-type Drinfeld–Sokolov hierarchy, i.e. a reduction of the dispersionless two-component BKP hierarchy, is studied. The additional symmetry flows of this hierarchy are presented. Thes...In this paper, the dispersionless D-type Drinfeld–Sokolov hierarchy, i.e. a reduction of the dispersionless two-component BKP hierarchy, is studied. The additional symmetry flows of this hierarchy are presented. These flows form an infinite-dimensional Lie algebra of Block type as well as a Lie algebra of Hamiltonian type.展开更多
We construct a class of new Lie algebras by generalizing the one-variable Lie algebras generated by the quadratic conformal algebras （or corresponding Hamiltonian operators） associated with Poisson algebras and a qu...We construct a class of new Lie algebras by generalizing the one-variable Lie algebras generated by the quadratic conformal algebras （or corresponding Hamiltonian operators） associated with Poisson algebras and a quasi-derivation found by Xu. These algebras can be viewed as certain twists of Xu＇s generalized Hamiltonian Lie algebras. The simplicity of these algebras is completely determined. Moreover, we construct a family of multiplicity-free representations of these Lie algebras and prove their irreducibility.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No.10471091)"One Hundred Talents Program"from University of Science and Technology of China
文摘We first prove that,for any generalized Hamiltonian type Lie algebra H,the first co- homology group H^1(H,H(?)H) is trivial.We then show that all Lie bialgebra structures on H are triangular.
基金Supported by the National Natural Science Foundation of China under Grant No.11201251the National Natural Science Foundation of China under Grant No.11271210+5 种基金Zhejiang Provincial Natural Science Foundation under Grant No.LY12A01007the Natural Science Foundation of Ningbo under Grant No.2013A610105K.C.Wong Magna Fund in Ningbo Universitythe National Science Foundation of China under Grant No.11371278the Shanghai Municipal Science and Technology Commission under Grant No.12XD1405000the Fundamental Research Funds for the Central Universities of China
文摘In this paper, the dispersionless D-type Drinfeld–Sokolov hierarchy, i.e. a reduction of the dispersionless two-component BKP hierarchy, is studied. The additional symmetry flows of this hierarchy are presented. These flows form an infinite-dimensional Lie algebra of Block type as well as a Lie algebra of Hamiltonian type.
基金Supported by National Natural Science Foundation of China （Grant No. 10871193）
文摘We construct a class of new Lie algebras by generalizing the one-variable Lie algebras generated by the quadratic conformal algebras （or corresponding Hamiltonian operators） associated with Poisson algebras and a quasi-derivation found by Xu. These algebras can be viewed as certain twists of Xu＇s generalized Hamiltonian Lie algebras. The simplicity of these algebras is completely determined. Moreover, we construct a family of multiplicity-free representations of these Lie algebras and prove their irreducibility.
