The simple modules for electrical Lie algebra of type D5 were investigated.The sufficient and necessary criteria of the simple Z-graded highest weight modules were established by means of determining the singular vect...The simple modules for electrical Lie algebra of type D5 were investigated.The sufficient and necessary criteria of the simple Z-graded highest weight modules were established by means of determining the singular vectors of the Verma modules.The simple highest weight module is isomorphic to either that for the symplectic Lie algebra sp4 or Verma module.展开更多
A root system is any collection of vectors that has properties that satisfy the roots of a semi simple Lie algebra. If g is semi simple, then the root system A, (Q) can be described as a system of vectors in a Euclide...A root system is any collection of vectors that has properties that satisfy the roots of a semi simple Lie algebra. If g is semi simple, then the root system A, (Q) can be described as a system of vectors in a Euclidean vector space that possesses some remarkable symmetries and completely defines the Lie algebra of g. The purpose of this paper is to show the essentiality of the root system on the Lie algebra. In addition, the paper will mention the connection between the root system and Ways chambers. In addition, we will show Dynkin diagrams, which are an integral part of the root system.展开更多
Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.
Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti-Johnson (GJ)hierarchy and the Yang hierarchy are obtained,respectively.By employing the variational identity t...Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti-Johnson (GJ)hierarchy and the Yang hierarchy are obtained,respectively.By employing the variational identity theirHamiltonian structures are also generated.The approach presented in the paper can also provide nonlinear integrablecouplings of other soliton hierarchies of evolution equations.展开更多
The finite-dimensional indecomposable solvable Lie algebras s with Q2n+1as their nilradical are studied and classified, it turns out that the dimension of s is dim Q2n+1+1.Then the Hom-Lie algebra structures on solvab...The finite-dimensional indecomposable solvable Lie algebras s with Q2n+1as their nilradical are studied and classified, it turns out that the dimension of s is dim Q2n+1+1.Then the Hom-Lie algebra structures on solvable Lie algebras s are calculated.展开更多
Advanced mathematical tools are used to conduct research on the kinematics analysis of hybrid mechanisms,and the generalized analysis method and concise kinematics transfer matrix are obtained.In this study,first,acco...Advanced mathematical tools are used to conduct research on the kinematics analysis of hybrid mechanisms,and the generalized analysis method and concise kinematics transfer matrix are obtained.In this study,first,according to the kinematics analysis of serial mechanisms,the basic principles of Lie groups and Lie algebras are briefly explained in dealing with the spatial switching and differential operations of screw vectors.Then,based on the standard ideas of Lie operations,the method for kinematics analysis of parallel mechanisms is derived,and Jacobian matrix and Hessian matrix are formulated recursively and in a closed form.Then,according to the mapping relationship between the parallel joints and corresponding equivalent series joints,a forward kinematics analysis method and two inverse kinematics analysis methods of hybrid mechanisms are examined.A case study is performed to verify the calculated matrices wherein a humanoid hybrid robotic arm with a parallel-series-parallel configuration is considered as an example.The results of a simulation experiment indicate that the obtained formulas are exact and the proposed method for kinematics analysis of hybrid mechanisms is practically feasible.展开更多
In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-...In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ■ _(ad~*) g~* and some new structures of left-symmetric algebra induced from g and its Rota-Baxter operators.展开更多
Let A be a factor von Neumann algebra and Φ be a nonlinear surjective map from A onto itself.We prove that,if Φ satisfies that Φ(A)Φ(B)-Φ(B)Φ(A)= AB-BA* for all A,B ∈ A,then there exist a linear bijective map ...Let A be a factor von Neumann algebra and Φ be a nonlinear surjective map from A onto itself.We prove that,if Φ satisfies that Φ(A)Φ(B)-Φ(B)Φ(A)= AB-BA* for all A,B ∈ A,then there exist a linear bijective map Ψ:A → A satisfying Ψ(A)Ψ(B)-Ψ(B)Ψ(A)= AB-BA* for A,B ∈A and a real functional h on A with h(0) = 0 such that Φ(A) = Ψ(A) + h(A)I for every A ∈A.In particular,if A is a type I factor,then,Φ(A) = cA + h(A)I for every A ∈ A,where c = ±1.展开更多
Non-commutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law.In this paper,the non-commutative poisson algebra structures on ...Non-commutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law.In this paper,the non-commutative poisson algebra structures on the Lie algebras sln(Cq)are determined.展开更多
In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer(L)and central extension H 2(L,F)on some Lie ...In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer(L)and central extension H 2(L,F)on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.展开更多
By using a six-dimensional matrix Lie algebra [Y.F.Zhang and Y.Wang,Phys.Lett.A 360 (2006) 92], three induced Lie algebras are constructed.One of them is obtained by extending Lie bracket,the others are higher- dimens...By using a six-dimensional matrix Lie algebra [Y.F.Zhang and Y.Wang,Phys.Lett.A 360 (2006) 92], three induced Lie algebras are constructed.One of them is obtained by extending Lie bracket,the others are higher- dimensional complex Lie algebras constructed by using linear transformations.The equivalent Lie algebras of the later two with multi-component forms are obtained as well.As their applications,we derive an integrable coupling and quasi-Hamiltonian structure of the modified TC hierarchy of soliton equations.展开更多
In this paper, we study the Lie algebras in which every subspace is its subalgebra (denoted by HB Lie algebras). We get that a nonabelian Lie algebra is an HB Lie algebra if and only if it is isomorphic to g +˙Cidg, ...In this paper, we study the Lie algebras in which every subspace is its subalgebra (denoted by HB Lie algebras). We get that a nonabelian Lie algebra is an HB Lie algebra if and only if it is isomorphic to g +˙Cidg, where g is an abelian Lie algebra. Moreover we show that the derivation algebra and the holomorph of a nonabelian HB Lie algebra are complete.展开更多
Let Mn be the algebra of all n × n complex matrices and gl(n, C) be the general linear Lie algebra, where n ≥ 2. An invertible linear map φ : gl(n, C) → gl(n, C) preserves solvability in both directions if bo...Let Mn be the algebra of all n × n complex matrices and gl(n, C) be the general linear Lie algebra, where n ≥ 2. An invertible linear map φ : gl(n, C) → gl(n, C) preserves solvability in both directions if both φ and φ-1 map every solvable Lie subalgebra of gl(n, C) to some solvable Lie subalgebra. In this paper we classify the invertible linear maps preserving solvability on gl(n, C) in both directions. As a sequence, such maps coincide with the invertible linear maps preserving commutativity on Mn in both directions.展开更多
In this paper,we mainly study some properties of elementary n-Lie algebras,and prove some necessary and sufficient conditions for elementary n-Lie algebras.We also give the relations between elementary n-algebras and ...In this paper,we mainly study some properties of elementary n-Lie algebras,and prove some necessary and sufficient conditions for elementary n-Lie algebras.We also give the relations between elementary n-algebras and E-algebras.展开更多
In this paper,we will give the definition of completable nilpotent Lie algebras,discuss its decomposition and prove that the heisenberg algebras and extensions of abelian quadratic Lie algebras are all completable nil...In this paper,we will give the definition of completable nilpotent Lie algebras,discuss its decomposition and prove that the heisenberg algebras and extensions of abelian quadratic Lie algebras are all completable nilpotent Lie algebras.展开更多
基金Fundamental Research Funds for the Central Universities,China(No.2232021G13)。
文摘The simple modules for electrical Lie algebra of type D5 were investigated.The sufficient and necessary criteria of the simple Z-graded highest weight modules were established by means of determining the singular vectors of the Verma modules.The simple highest weight module is isomorphic to either that for the symplectic Lie algebra sp4 or Verma module.
文摘A root system is any collection of vectors that has properties that satisfy the roots of a semi simple Lie algebra. If g is semi simple, then the root system A, (Q) can be described as a system of vectors in a Euclidean vector space that possesses some remarkable symmetries and completely defines the Lie algebra of g. The purpose of this paper is to show the essentiality of the root system on the Lie algebra. In addition, the paper will mention the connection between the root system and Ways chambers. In addition, we will show Dynkin diagrams, which are an integral part of the root system.
文摘Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.
基金Supported by the Fundamental Research Funds of the Central University under Grant No. 2010LKS808the Natural Science Foundation of Shandong Province under Grant No. ZR2009AL021
文摘Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti-Johnson (GJ)hierarchy and the Yang hierarchy are obtained,respectively.By employing the variational identity theirHamiltonian structures are also generated.The approach presented in the paper can also provide nonlinear integrablecouplings of other soliton hierarchies of evolution equations.
基金Foundation item: Supported by the National Natural Science Foundation of China(11071187) Supported by the Natural Science Foundation of Henan Province(13A110785)
文摘The finite-dimensional indecomposable solvable Lie algebras s with Q2n+1as their nilradical are studied and classified, it turns out that the dimension of s is dim Q2n+1+1.Then the Hom-Lie algebra structures on solvable Lie algebras s are calculated.
基金Supported by Zhejiang Province Foundation for Distinguished Young Scholars of China(Grant No.LR18E050003)National Natural Science Foundation of China(Grant Nos.51975523,51475424,51905481)Open Foundation of the State Key Laboratory of Fluid Power and Mechatronic Systems(Grant No.GZKF-201906).
文摘Advanced mathematical tools are used to conduct research on the kinematics analysis of hybrid mechanisms,and the generalized analysis method and concise kinematics transfer matrix are obtained.In this study,first,according to the kinematics analysis of serial mechanisms,the basic principles of Lie groups and Lie algebras are briefly explained in dealing with the spatial switching and differential operations of screw vectors.Then,based on the standard ideas of Lie operations,the method for kinematics analysis of parallel mechanisms is derived,and Jacobian matrix and Hessian matrix are formulated recursively and in a closed form.Then,according to the mapping relationship between the parallel joints and corresponding equivalent series joints,a forward kinematics analysis method and two inverse kinematics analysis methods of hybrid mechanisms are examined.A case study is performed to verify the calculated matrices wherein a humanoid hybrid robotic arm with a parallel-series-parallel configuration is considered as an example.The results of a simulation experiment indicate that the obtained formulas are exact and the proposed method for kinematics analysis of hybrid mechanisms is practically feasible.
基金The NSF(11047030 and 11771122) of Chinathe Science and Technology Program(152300410061) of Henan Province
文摘In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ■ _(ad~*) g~* and some new structures of left-symmetric algebra induced from g and its Rota-Baxter operators.
基金supported by National Natural Science Foundation of China(10871111)the Specialized Research Fund for Doctoral Program of Higher Education(200800030059)(to Cui)Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education,Science and Technology(NRF-2009-0070788)(to Park)
文摘Let A be a factor von Neumann algebra and Φ be a nonlinear surjective map from A onto itself.We prove that,if Φ satisfies that Φ(A)Φ(B)-Φ(B)Φ(A)= AB-BA* for all A,B ∈ A,then there exist a linear bijective map Ψ:A → A satisfying Ψ(A)Ψ(B)-Ψ(B)Ψ(A)= AB-BA* for A,B ∈A and a real functional h on A with h(0) = 0 such that Φ(A) = Ψ(A) + h(A)I for every A ∈A.In particular,if A is a type I factor,then,Φ(A) = cA + h(A)I for every A ∈ A,where c = ±1.
基金supported by NSF of China(11071187)Innovation Program of Shanghai Municipal Education Commission(09YZ336)
文摘Non-commutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law.In this paper,the non-commutative poisson algebra structures on the Lie algebras sln(Cq)are determined.
基金National Natural Science Foundation of China(10271076)
文摘In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer(L)and central extension H 2(L,F)on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.
文摘By using a six-dimensional matrix Lie algebra [Y.F.Zhang and Y.Wang,Phys.Lett.A 360 (2006) 92], three induced Lie algebras are constructed.One of them is obtained by extending Lie bracket,the others are higher- dimensional complex Lie algebras constructed by using linear transformations.The equivalent Lie algebras of the later two with multi-component forms are obtained as well.As their applications,we derive an integrable coupling and quasi-Hamiltonian structure of the modified TC hierarchy of soliton equations.
文摘In this paper, we study the Lie algebras in which every subspace is its subalgebra (denoted by HB Lie algebras). We get that a nonabelian Lie algebra is an HB Lie algebra if and only if it is isomorphic to g +˙Cidg, where g is an abelian Lie algebra. Moreover we show that the derivation algebra and the holomorph of a nonabelian HB Lie algebra are complete.
基金The NSF (2009J05005) of Fujian Provincea Key Project of Fujian Provincial Universities-Information Technology Research Based on Mathematics
文摘Let Mn be the algebra of all n × n complex matrices and gl(n, C) be the general linear Lie algebra, where n ≥ 2. An invertible linear map φ : gl(n, C) → gl(n, C) preserves solvability in both directions if both φ and φ-1 map every solvable Lie subalgebra of gl(n, C) to some solvable Lie subalgebra. In this paper we classify the invertible linear maps preserving solvability on gl(n, C) in both directions. As a sequence, such maps coincide with the invertible linear maps preserving commutativity on Mn in both directions.
基金The NSF(A2007000138,2005000088)of Hebei Provincethe NSF(y2004034)of Hebei University
文摘In this paper,we mainly study some properties of elementary n-Lie algebras,and prove some necessary and sufficient conditions for elementary n-Lie algebras.We also give the relations between elementary n-algebras and E-algebras.
基金The project supported by National Natural Science Foundation of China under Grant Nos.10471139,10371023Shanghai Shuguang Project under Grant No.02SG02
基金Supported by National Science Foundation of Jiangau.
文摘In this paper,we will give the definition of completable nilpotent Lie algebras,discuss its decomposition and prove that the heisenberg algebras and extensions of abelian quadratic Lie algebras are all completable nilpotent Lie algebras.