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
Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent m...Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent manifolds. So we start with the differential sequence of Lie algebras. The Lie algebra g has the differential sequence E0,E1,⋯,Es⋯, which leads to the chain complex Es0→Δs0Ess→Δs1⋯→ΔsiEs(i+1)s→Δsi+1⋯of Esby discussing the chain complex E10→Δ10E11→Δ11⋯→Δ1r−1E1r→Δ1r⋯of E1and proves that Es+1i≅Hi(Es)=KerΔsi+1/ImΔsiand therefore Es+1≅H(Es)by the chain complex of Es(see Theorem 2).展开更多
In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better...In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.展开更多
We mainly study the super-biderivations of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras.In particular,we prove that all super-biderivations of not-finitely graded Lie superalgeb...We mainly study the super-biderivations of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras.In particular,we prove that all super-biderivations of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras are inner.展开更多
In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations an...In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic.In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive(implicative)derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97-113] and [Information Sciences, 178(2008),307-316].展开更多
We introduce and investigate the properties of a generalization of the derivation of dendriform algebras. We specify all possible parameter values for the generalized derivations, which depend on parameters. We provid...We introduce and investigate the properties of a generalization of the derivation of dendriform algebras. We specify all possible parameter values for the generalized derivations, which depend on parameters. We provide all generalized derivations for complex low-dimensional dendriform algebras.展开更多
The aim of this paper is to outline the conditions of a conformal hyperquaternion algebra H<sup>⊗2m</sup> in which a higher order plane curve can be described by generalizing the well-known cases of conics...The aim of this paper is to outline the conditions of a conformal hyperquaternion algebra H<sup>⊗2m</sup> in which a higher order plane curve can be described by generalizing the well-known cases of conics and cubic curves in 2D. In other words, the determination of the order of a plane curve through n points and its conformal hyperquaternion algebra H<sup>⊗2m</sup> is the object of this work.展开更多
A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-L...A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.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
Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bound...Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L<sup>∞</sup>(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L<sup>2</sup>(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .展开更多
In this paper, from the spacetime algebra associated with the Minkowski space ℝ3,1by means of a change of signature, we describe a quaternionic representation of the split-tetraquaternion algebra which incorporates th...In this paper, from the spacetime algebra associated with the Minkowski space ℝ3,1by means of a change of signature, we describe a quaternionic representation of the split-tetraquaternion algebra which incorporates the Pauli algebra, the split-biquaternion algebra and the split-quaternion algebra, we relate these algebras to Clifford algebras and we show the emergence of the stabilized Poincaré-Heisenberg algebra from the split-tetraquaternion algebra. We list without going into details some of their applications in Physics and in Born geometry.展开更多
The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers ...The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers would only provide dramatic speedups for a few specific problems, for example, factoring integers and breaking cryptographic codes in the conventional quantum computing approach. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In the conventional approach, it is implemented through the tensor product of qubits. In the suggested geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on a three-dimensional sphere, which is very different from the usual Hilbert space scheme.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.
Some basic properties of the antipode of an N0I-graded x-Hopf algebra are studied. Also, several equivalent conditions of an N0I-graded x-bialgebra (x-Hopf algebra) are given.
The variety ddpM of de Morgan algebras with double demi-pseudocomplementation consists of those algebras (L; ∧ , ∨ , , , + , 0, 1) of type (2, 2, 1, 1, 1, 0, 0) where (L; ∧ , ∨ , , 0, 1) is a de Morgan alge...The variety ddpM of de Morgan algebras with double demi-pseudocomplementation consists of those algebras (L; ∧ , ∨ , , , + , 0, 1) of type (2, 2, 1, 1, 1, 0, 0) where (L; ∧ , ∨ , , 0, 1) is a de Morgan algebra, (L; ∧ , ∨ , , + , 0, 1) is a double demi-p-lattice and the operations x → x , x → x and x → x + are linked by the identities x = x , x + = x + and x + = x + . In this paper, we characterize congruences on a ddpM-algebra, and give a description of the subdirectly irreducible algebras.展开更多
This paper gives a sufficient and necessary condition for twisted products to be weak Hopf algebras, moreover, gives a description for smash products to be weak Hopf algebras. It respectively generalizes R.K.Molnar...This paper gives a sufficient and necessary condition for twisted products to be weak Hopf algebras, moreover, gives a description for smash products to be weak Hopf algebras. It respectively generalizes R.K.Molnar's major result and I.Boca's result.展开更多
In this paper, we prove that any nonlinear Jordan higher derivation on triangular algebras is an additive higher derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algebras over infinit...In this paper, we prove that any nonlinear Jordan higher derivation on triangular algebras is an additive higher derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algebras over infinite dimensional Hilbert suaces is inner.展开更多
Let A be a factor von Neumann algebra and Ф be a nonlinear surjective map from A onto itself. We prove that, if Ф satisfies that Ф(A)Ф(B) - Ф(B)Ф(A)* -- AB - BA* for all A, B ∈ A, then there exist a l...Let A be a factor von Neumann algebra and Ф be a nonlinear surjective map from A onto itself. We prove that, if Ф satisfies that Ф(A)Ф(B) - Ф(B)Ф(A)* -- AB - BA* for all A, B ∈ A, then there exist a linear bijective map ψA →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 Ф(A) = ψ(A) + h(A)I for every A ∈ A. In particular, if .4 is a type I factor, then, Ф(A) = cA + h(A)I for every A ∈ .4, where c = ±1.展开更多
In this paper,the topological space(PF_(MP)(X),T) based on prime MP-filters of a lattice FI-algebra X is constructed firstly and we proved that it is a compact T_0-space if X with condition(P).Secondly,we restricted T...In this paper,the topological space(PF_(MP)(X),T) based on prime MP-filters of a lattice FI-algebra X is constructed firstly and we proved that it is a compact T_0-space if X with condition(P).Secondly,we restricted T to the set of all maximal MP-filters MF_(MP)(X) of X and concluded that(PF_(MP)(X),T |_(PF_(MP)(X)) )is a compact T_2 space if X with conditions(P) and(S).展开更多
Let A be a subalgebra of B(X) containing the identity operator I and an idempotent P. Suppose that α,β: A →A are ring epimorphisms and there exists some nest N on 2( such that α(P)(X) and β(P)(X) are ...Let A be a subalgebra of B(X) containing the identity operator I and an idempotent P. Suppose that α,β: A →A are ring epimorphisms and there exists some nest N on 2( such that α(P)(X) and β(P)(X) are non-trivial elements of N. Let A contain all rank one operators in AlgN and δ : A→ B(X) be an additive mapping. It is shown that, if δ is (α, β)-derivable at zero point, then there exists an additive (α, β)-derivation τ : A →β(X) such that δ(A) =τ(A) + α(A)δ(I) for all A∈A. It is also shown that if δ is generalized (α,β)-derivable at zero point, then δ is an additive generalized (α, β)-derivation. Moreover, by use of this result, the additive maps (generalized) (α,β)-derivable at zero point on several nest algebras, are also characterized.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Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent manifolds. So we start with the differential sequence of Lie algebras. The Lie algebra g has the differential sequence E0,E1,⋯,Es⋯, which leads to the chain complex Es0→Δs0Ess→Δs1⋯→ΔsiEs(i+1)s→Δsi+1⋯of Esby discussing the chain complex E10→Δ10E11→Δ11⋯→Δ1r−1E1r→Δ1r⋯of E1and proves that Es+1i≅Hi(Es)=KerΔsi+1/ImΔsiand therefore Es+1≅H(Es)by the chain complex of Es(see Theorem 2).
基金partially supported by the Natural Sciences and Engineering Research Council of Canada(2019-03907)。
文摘In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.11601135,11701158,11771069)the Natural Science Foundation of Heilongjiang Province of China(Grant Nos.QC2017002,LH2020A020)the Project funded by China Postdoctoral Science Foundation(Grant No.2018M630311).
文摘We mainly study the super-biderivations of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras.In particular,we prove that all super-biderivations of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras are inner.
基金Supported by a grant of National Natural Science Foundation of China(12001243,61976244,12171294,11961016)the Natural Science Basic Research Plan in Shaanxi Province of China(2020JQ-762,2021JQ-580)。
文摘In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic.In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive(implicative)derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97-113] and [Information Sciences, 178(2008),307-316].
文摘We introduce and investigate the properties of a generalization of the derivation of dendriform algebras. We specify all possible parameter values for the generalized derivations, which depend on parameters. We provide all generalized derivations for complex low-dimensional dendriform algebras.
文摘The aim of this paper is to outline the conditions of a conformal hyperquaternion algebra H<sup>⊗2m</sup> in which a higher order plane curve can be described by generalizing the well-known cases of conics and cubic curves in 2D. In other words, the determination of the order of a plane curve through n points and its conformal hyperquaternion algebra H<sup>⊗2m</sup> is the object of this work.
基金Supported by the National Natural Science Foundation of China(11501523,61673320)。
文摘A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.
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Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L<sup>∞</sup>(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L<sup>2</sup>(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .
文摘In this paper, from the spacetime algebra associated with the Minkowski space ℝ3,1by means of a change of signature, we describe a quaternionic representation of the split-tetraquaternion algebra which incorporates the Pauli algebra, the split-biquaternion algebra and the split-quaternion algebra, we relate these algebras to Clifford algebras and we show the emergence of the stabilized Poincaré-Heisenberg algebra from the split-tetraquaternion algebra. We list without going into details some of their applications in Physics and in Born geometry.
文摘The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers would only provide dramatic speedups for a few specific problems, for example, factoring integers and breaking cryptographic codes in the conventional quantum computing approach. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In the conventional approach, it is implemented through the tensor product of qubits. In the suggested geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on a three-dimensional sphere, which is very different from the usual Hilbert space scheme.
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This paper is supported by the Chinese National Natural Science Foundation
文摘Some basic properties of the antipode of an N0I-graded x-Hopf algebra are studied. Also, several equivalent conditions of an N0I-graded x-bialgebra (x-Hopf algebra) are given.
文摘The variety ddpM of de Morgan algebras with double demi-pseudocomplementation consists of those algebras (L; ∧ , ∨ , , , + , 0, 1) of type (2, 2, 1, 1, 1, 0, 0) where (L; ∧ , ∨ , , 0, 1) is a de Morgan algebra, (L; ∧ , ∨ , , + , 0, 1) is a double demi-p-lattice and the operations x → x , x → x and x → x + are linked by the identities x = x , x + = x + and x + = x + . In this paper, we characterize congruences on a ddpM-algebra, and give a description of the subdirectly irreducible algebras.
基金This work is supported by National Natural Science Foundation of Chinaby the excellent doctorate fund of Nanjing agricultural university
文摘This paper gives a sufficient and necessary condition for twisted products to be weak Hopf algebras, moreover, gives a description for smash products to be weak Hopf algebras. It respectively generalizes R.K.Molnar's major result and I.Boca's result.
文摘In this paper, we prove that any nonlinear Jordan higher derivation on triangular algebras is an additive higher derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algebras over infinite dimensional Hilbert suaces is inner.
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 Ф be a nonlinear surjective map from A onto itself. We prove that, if Ф satisfies that Ф(A)Ф(B) - Ф(B)Ф(A)* -- AB - BA* for all A, B ∈ A, then there exist a linear bijective map ψA →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 Ф(A) = ψ(A) + h(A)I for every A ∈ A. In particular, if .4 is a type I factor, then, Ф(A) = cA + h(A)I for every A ∈ .4, where c = ±1.
基金Supported by the NSF of China(10371106,60774073)
文摘In this paper,the topological space(PF_(MP)(X),T) based on prime MP-filters of a lattice FI-algebra X is constructed firstly and we proved that it is a compact T_0-space if X with condition(P).Secondly,we restricted T to the set of all maximal MP-filters MF_(MP)(X) of X and concluded that(PF_(MP)(X),T |_(PF_(MP)(X)) )is a compact T_2 space if X with conditions(P) and(S).
文摘Let A be a subalgebra of B(X) containing the identity operator I and an idempotent P. Suppose that α,β: A →A are ring epimorphisms and there exists some nest N on 2( such that α(P)(X) and β(P)(X) are non-trivial elements of N. Let A contain all rank one operators in AlgN and δ : A→ B(X) be an additive mapping. It is shown that, if δ is (α, β)-derivable at zero point, then there exists an additive (α, β)-derivation τ : A →β(X) such that δ(A) =τ(A) + α(A)δ(I) for all A∈A. It is also shown that if δ is generalized (α,β)-derivable at zero point, then δ is an additive generalized (α, β)-derivation. Moreover, by use of this result, the additive maps (generalized) (α,β)-derivable at zero point on several nest algebras, are also characterized.