The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the h...The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the homogeneous components of degree zero of the third cohomology group of Lie color algebras. As an application of this theory, the crossed modules of Witt type Lie color algebras is described, and the result is proved that there is only one equivalent class of the crossed modules of Witt type Lie color algebras when the abelian group Г is equal to Г＋. Finally, for a Witt type Lie color algebra, the classification of its crossed modules is obtained by the isomorphism between the third cohomology group and the crossed modules.展开更多
A bosonic construction (with central charge c = 2) of Lie algebras W1+∞ and W1+∞ (glN), as well as the decompositions into irreducible modules are described. And for W1+∞, when restricted to its Virasoro subalgebra...A bosonic construction (with central charge c = 2) of Lie algebras W1+∞ and W1+∞ (glN), as well as the decompositions into irreducible modules are described. And for W1+∞, when restricted to its Virasoro subalgebra Vir, a bosonic construction and the same decomposition for Vir are obtained.展开更多
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
基金The Natural Science Foundation of Jiangsu Province(No.BK2012736)the Natural Science Foundation of Chuzhou University(No.2010kj006Z)
文摘The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the homogeneous components of degree zero of the third cohomology group of Lie color algebras. As an application of this theory, the crossed modules of Witt type Lie color algebras is described, and the result is proved that there is only one equivalent class of the crossed modules of Witt type Lie color algebras when the abelian group Г is equal to Г＋. Finally, for a Witt type Lie color algebra, the classification of its crossed modules is obtained by the isomorphism between the third cohomology group and the crossed modules.
基金Project supported by the National Natural Science Foundation of China (No. 10431040, No.10271047, No.19731004) the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institution of the Ministry of Education of China, the Specialized Research Fund for the Doctoral Program of Higher Education of the Ministry of Education of China, the Shanghai Rising-Star Program of the Science and Technology Commission of Shanghai and the Shanghai Priority Academic Discipline of the Education Commission of Shanghai.
文摘A bosonic construction (with central charge c = 2) of Lie algebras W1+∞ and W1+∞ (glN), as well as the decompositions into irreducible modules are described. And for W1+∞, when restricted to its Virasoro subalgebra Vir, a bosonic construction and the same decomposition for Vir are obtained.
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.
