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
For any additive subgroup M of a field F and α∈F such that 2α∈M ,there are two classes of generalized super-Virasoro algebras denoted by SVir [M,α] and SVir [M,α] by Su and Zhao. The latter is in fact a tr...For any additive subgroup M of a field F and α∈F such that 2α∈M ,there are two classes of generalized super-Virasoro algebras denoted by SVir [M,α] and SVir [M,α] by Su and Zhao. The latter is in fact a trivial extension of the former. In this paper,based on the discussion on isomorphisms,the Verma modules of Svir [ M,α] are studied,and the irreducibility of these modules are obtained.展开更多
Firstly we expand a finite-dimensional Lie algebra into a higher-dimenslonal one. By making use of the later and its corresponding loop algebra, the expanding integrable model of the multi-component NLS-mKdV hierarchy...Firstly we expand a finite-dimensional Lie algebra into a higher-dimenslonal one. By making use of the later and its corresponding loop algebra, the expanding integrable model of the multi-component NLS-mKdV hierarchy is worked out.展开更多
A new Lax integrable hierarchy is obtained by constructing an isospectraJ problem with constrained conditions. Two kinds of integrable couplings are obtained by constructing two new expanding Lie algebras of the Lie a...A new Lax integrable hierarchy is obtained by constructing an isospectraJ problem with constrained conditions. Two kinds of integrable couplings are obtained by constructing two new expanding Lie algebras of the Lie algebra Be, respectively.展开更多
By means of a simple ideal, which is firstly proposed for the continuous system, we present an arbitrary order classical Toda family invariant under common Virasoro-type symmetry algebra.
This gives some identities of associative Lie superalgebras and some properties of modular Lie superalgebras. Furthermore, the primary decomposition theorem of modular Lie superalgebras is shown. It is well known that...This gives some identities of associative Lie superalgebras and some properties of modular Lie superalgebras. Furthermore, the primary decomposition theorem of modular Lie superalgebras is shown. It is well known that the primary decomposition theorem of modular Lie algebras has played an important role in the classification of the finite-dimensional simple modular Lie algebras （see [5, 6]）. Analogously, the primary decomposition theorem of modular Lie superalgebras may play an important role in the open classification of the finite dimensional simple modular Lie superalgebras.展开更多
For any complex parameters a and b,W(a,b)is the Lie algebra with basis{Li,Wi|i∈Z}and relations[Li,Lj]=(j i)Li+j,[Li,Wj]=(a+j+bi)Wi+j,[Wi,Wj]=0.In this paper,indecomposable modules of the intermediate series over W(a,...For any complex parameters a and b,W(a,b)is the Lie algebra with basis{Li,Wi|i∈Z}and relations[Li,Lj]=(j i)Li+j,[Li,Wj]=(a+j+bi)Wi+j,[Wi,Wj]=0.In this paper,indecomposable modules of the intermediate series over W(a,b)are classified.It is also proved that an irreducible Harish-Chandra W(a,b)-module is either a highest/lowest weight module or a uniformly bounded module.Furthermore,if a∈/Q,an irreducible weight W(a,b)-module is simply a Vir-module with trivial actions of Wk’s.展开更多
Let F be an algebraically closed field of prime characteristic p>3,and W(n)the Witt superalgebra over F,which is the Lie superalgebra of superderivations of the Grassmann algebra in n indeterminates.The dimensions ...Let F be an algebraically closed field of prime characteristic p>3,and W(n)the Witt superalgebra over F,which is the Lie superalgebra of superderivations of the Grassmann algebra in n indeterminates.The dimensions of simple atypical modules in the restricted supermodule category for W(n)are precisely calculated in this paper,and thereby the dimensions of all simple modules can be precisely given.Moreover,the restricted supermodule category for W(n)is proved to have one block.展开更多
We construct a class of modules for extended affine Lie algebra gl l（Cq） by using the free fields. A necessary and sufficient condition is given for those modules being irreducible.
The authors consider a family of finite-dimensional Lie superalgebras of C-type over an algebraically closed field of characteristic p 〉 3. It is proved that the Lie superalgebras of C-type are simple and the spannin...The authors consider a family of finite-dimensional Lie superalgebras of C-type over an algebraically closed field of characteristic p 〉 3. It is proved that the Lie superalgebras of C-type are simple and the spanning sets are determined. Then the spanning sets are employed to characterize the superderivation algebras of these Lie superalgebras. Finally, the associative forms are discussed and a comparison is made between these Lie superalgebras and other simple Lie superalgebras of Cartan type.展开更多
We show that the denominator identity for ortho-symplectic Lie superalgebras 0sp（kl2n） is equiva- lent to the Littlewood＇s formula. Such an equivalence also implies the relation between the trivial module and gener...We show that the denominator identity for ortho-symplectic Lie superalgebras 0sp（kl2n） is equiva- lent to the Littlewood＇s formula. Such an equivalence also implies the relation between the trivial module and generalized Verma modules for op（kl2n）. Furthermore, we discuss the harmonic representative elements of the Kostant＇s u-cohomology with trivial coefficients.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TheNationalNaturalScienceFoundationofChina (No .10 1710 64 )
文摘For any additive subgroup M of a field F and α∈F such that 2α∈M ,there are two classes of generalized super-Virasoro algebras denoted by SVir [M,α] and SVir [M,α] by Su and Zhao. The latter is in fact a trivial extension of the former. In this paper,based on the discussion on isomorphisms,the Verma modules of Svir [ M,α] are studied,and the irreducibility of these modules are obtained.
基金The authors are very grateful to professor Yu-Feng Zhang for his ardent guidance and help.
文摘Firstly we expand a finite-dimensional Lie algebra into a higher-dimenslonal one. By making use of the later and its corresponding loop algebra, the expanding integrable model of the multi-component NLS-mKdV hierarchy is worked out.
基金Supported by National Natural Science Foundation of China under Grant No. 70971079
文摘A new Lax integrable hierarchy is obtained by constructing an isospectraJ problem with constrained conditions. Two kinds of integrable couplings are obtained by constructing two new expanding Lie algebras of the Lie algebra Be, respectively.
文摘By means of a simple ideal, which is firstly proposed for the continuous system, we present an arbitrary order classical Toda family invariant under common Virasoro-type symmetry algebra.
基金Project supported by the National Natural Science Foundation of China (No.10271076) the Youth Science Foundation of Northeast Normal University (No. 111494027).
文摘This gives some identities of associative Lie superalgebras and some properties of modular Lie superalgebras. Furthermore, the primary decomposition theorem of modular Lie superalgebras is shown. It is well known that the primary decomposition theorem of modular Lie algebras has played an important role in the classification of the finite-dimensional simple modular Lie algebras （see [5, 6]）. Analogously, the primary decomposition theorem of modular Lie superalgebras may play an important role in the open classification of the finite dimensional simple modular Lie superalgebras.
基金supported by National Natural Science Foundation of China(Grant Nos.11371287,11301130,11001200 and 11101269)the Fundamental Research Funds for the Central Universities Shanghai Municipal Science and Technology Commission(Grant No.12XD1405000)
文摘For any complex parameters a and b,W(a,b)is the Lie algebra with basis{Li,Wi|i∈Z}and relations[Li,Lj]=(j i)Li+j,[Li,Wj]=(a+j+bi)Wi+j,[Wi,Wj]=0.In this paper,indecomposable modules of the intermediate series over W(a,b)are classified.It is also proved that an irreducible Harish-Chandra W(a,b)-module is either a highest/lowest weight module or a uniformly bounded module.Furthermore,if a∈/Q,an irreducible weight W(a,b)-module is simply a Vir-module with trivial actions of Wk’s.
基金supported by the National Natural Science Foundation of China(Nos.11126062,11201293,11226327,11271130)the Innovation Program of Shanghai Municipal Education Commission(Nos.12ZZ038,13YZ077)
文摘Let F be an algebraically closed field of prime characteristic p>3,and W(n)the Witt superalgebra over F,which is the Lie superalgebra of superderivations of the Grassmann algebra in n indeterminates.The dimensions of simple atypical modules in the restricted supermodule category for W(n)are precisely calculated in this paper,and thereby the dimensions of all simple modules can be precisely given.Moreover,the restricted supermodule category for W(n)is proved to have one block.
基金supported by National Natural Science Foundation of China (Grant Nos.10726014, 10801010)
文摘We construct a class of modules for extended affine Lie algebra gl l（Cq） by using the free fields. A necessary and sufficient condition is given for those modules being irreducible.
基金supported by the National Natural Science Foundation of China(No.11371182)the PhD Start-up Foundation of Liaoning University of China(No.2012002)the Predeclaration Fund of State Project of Liaoning University(No.2014LDGY01)
文摘The authors consider a family of finite-dimensional Lie superalgebras of C-type over an algebraically closed field of characteristic p 〉 3. It is proved that the Lie superalgebras of C-type are simple and the spanning sets are determined. Then the spanning sets are employed to characterize the superderivation algebras of these Lie superalgebras. Finally, the associative forms are discussed and a comparison is made between these Lie superalgebras and other simple Lie superalgebras of Cartan type.
基金supported by National Natural Science Foundation of China(Grant Nos.11101436 and 11101151)the Fundamental Research Funds for the Central Universities
文摘We show that the denominator identity for ortho-symplectic Lie superalgebras 0sp（kl2n） is equiva- lent to the Littlewood＇s formula. Such an equivalence also implies the relation between the trivial module and generalized Verma modules for op（kl2n）. Furthermore, we discuss the harmonic representative elements of the Kostant＇s u-cohomology with trivial coefficients.
