The filtration structure of finite-dimensional special odd Hamilton superalgebras over a field of prime characteristic was studied. By determining ad-nilpotent dements in the even part, the natural filtration of speci...The filtration structure of finite-dimensional special odd Hamilton superalgebras over a field of prime characteristic was studied. By determining ad-nilpotent dements in the even part, the natural filtration of special odd Hamiltonian superalgebras is proved to be invariant. Using this result, the special odd Hamilton superalgebras is classified. Finally, the automorphism group of the restricted special odd Hamilton superalgebras is determined.展开更多
A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgeb...A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapφon P is commuting if and only if φ is a scalar multiplication map on P.展开更多
In the paper we will give a complete classification of finite-dimemsional simple Novikov algebras over an algebraically closed field with prime characteristic p>2.
We study the variety of binary Lie algebras defined by the identities x^(2)=J(x,y,zu)=0,where J(a,b,c)denotes the Jacobian of a,b,c.Building on previous work by Carrillo,Rasskazova,Sabinina and Grishkov,in the present...We study the variety of binary Lie algebras defined by the identities x^(2)=J(x,y,zu)=0,where J(a,b,c)denotes the Jacobian of a,b,c.Building on previous work by Carrillo,Rasskazova,Sabinina and Grishkov,in the present article it is shown that the Levi and Malcev theorems hold for this variety of algebras.展开更多
The fact that infinite-dimensional algebra exists in a 2-dimensional Lax-pair system has caused keen interest.Using a variety of particular models, many explicit expressions have already been derived. Since the hidden...The fact that infinite-dimensional algebra exists in a 2-dimensional Lax-pair system has caused keen interest.Using a variety of particular models, many explicit expressions have already been derived. Since the hidden symmetry algebra was introduced in principal chiral model, the study of axially symmetric gravity with展开更多
Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algeb...Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algebras and tri-associative algebras.We introduce the notion of a quad-dendriform algebra,which is a splitting of a di-associative algebra.We show that a relative averaging operator on dendriform algebras gives rise to a quad-dendriform algebra.Furthermore,we introduce the notion of six-dendriform algebras,which are splittings of the tri-associative algebras,and demonstrate that homomorphic relative averaging operators induce six-dendriform algebras.展开更多
Lie algebras are special Leibniz algebras,so it is natural to view Lie algebras as Leibniz algebras.In this paper,we calculate all the Leibniz 2 cocycles of the Lie algebra K(1,0),which is helpful to classify one dime...Lie algebras are special Leibniz algebras,so it is natural to view Lie algebras as Leibniz algebras.In this paper,we calculate all the Leibniz 2 cocycles of the Lie algebra K(1,0),which is helpful to classify one dimensional central extensions of K(1,0)as Leibniz algebra.展开更多
This paper explores the algebraic essence of universal logic functions(ULFs)from an algebraic perspective.Under the framework of semi-tensor product of matrices,the“sequential nature”of ULFs is revealed.Utilizing th...This paper explores the algebraic essence of universal logic functions(ULFs)from an algebraic perspective.Under the framework of semi-tensor product of matrices,the“sequential nature”of ULFs is revealed.Utilizing the nature,a technique called universal transformation method is proposed,by which any ULF can be transformed into an equivalent expression with desired features that facilitate achieving specific objectives,such as modeling,analyzing and synthesizing universal logical systems.Furthermore,several useful logical operators are constructed in a mixed-dimensional situation,including power-raising operator,power-descending operator,erasure operator,and appending operator.Finally,these results are applied to model and analyze finite state machines and their networks,which demonstrate the practical value of the method and operators.展开更多
The well-known multi-dimensional reconciliation is an effective method used in the continuous-variable quantum key distribution in the long-distance and the low signal-to-noise-ratio scenarios.The virtual channel empl...The well-known multi-dimensional reconciliation is an effective method used in the continuous-variable quantum key distribution in the long-distance and the low signal-to-noise-ratio scenarios.The virtual channel employed to exchange data is generally established by using a finite-dimensional rotation in the reconciliation procedure.In this paper,we found that the finite dimension of the multi-dimensional reconciliation inevitably leads to the mismatch of the signal-to-noise-ratio between the quantum channel and the virtual channel,which may be called the finite-dimension effect.Such an effect results in an overestimation on the secret key rate,and subsequently induces vital practical security loopholes.展开更多
A new concept of convergence （R-convergence） of a sequence of measures is applied to characterize global minimizers in a functional space as a sequence of approximate solutions in finite-dimensional spaces. A deviat...A new concept of convergence （R-convergence） of a sequence of measures is applied to characterize global minimizers in a functional space as a sequence of approximate solutions in finite-dimensional spaces. A deviation integral approach is used to find such solutions. For a constrained problem, a penalized deviation integral algorithm is proposed to convert it to unconstrained ones. A numerical example on an optimal control problem with non-convex state constraints is given to show the effectiveness of the algorithm.展开更多
We theoretically analyze the photon number distribution,entanglement entropy,and Wigner phase-space distribution,considering the finite-dimensional pair coherent state(FDPCS)generated in the nonlinear Bose operator re...We theoretically analyze the photon number distribution,entanglement entropy,and Wigner phase-space distribution,considering the finite-dimensional pair coherent state(FDPCS)generated in the nonlinear Bose operator realization.Our results show that the photon number distribution is governed by the two-mode photon number sum q of the FDPCS,the entanglement of the FDPCS always increases quickly at first and then decreases slowly for any q,and the nonclassicality of the FDPCS for odd q is more stronger than that for even q.展开更多
This paper discusses the properties of amplitude-squared squeezing of the generalized odd-even coherent states of anharmonic oscillator in finite-dimensional Hilbert space. It demonstrates that the generalized odd coh...This paper discusses the properties of amplitude-squared squeezing of the generalized odd-even coherent states of anharmonic oscillator in finite-dimensional Hilbert space. It demonstrates that the generalized odd coherent states do exhibit strong amplitude-squared squeezing effects in comparison with the generalized even coherent states.展开更多
In this paper, we demonstrate that the finite-dimensional approximations to the solutions of a linear bond-based peridynamic boundary value problem converge to the exact solution exponentially with the analyticity ass...In this paper, we demonstrate that the finite-dimensional approximations to the solutions of a linear bond-based peridynamic boundary value problem converge to the exact solution exponentially with the analyticity assumption of the forcing term, therefore greatly improve the convergence rate derived in literature.展开更多
This paper constructs a new type of finite-dimensional thermal coherent states （FDTCS）, which differs from the proceeding thermal coherent state in construction, as realisations of SU（2） Lie algebra. Using the tec...This paper constructs a new type of finite-dimensional thermal coherent states （FDTCS）, which differs from the proceeding thermal coherent state in construction, as realisations of SU（2） Lie algebra. Using the technique of integration within an ordered product of operator, it investigates the orthonormality and completeness relation of the FDTCS. Based on the thermal Wigner operator in the thermal entangled state representation, the Wigner function of the FDTCS is obtained. The nonclassical properties of the FDTCS are discussed in terms of the negativity of its Wigner function.展开更多
In this paper a new class of finite-dimensional even and odd nonlinear pair coherent states （EONLPCSs）, which can be realized via operating the superposed evolution operators D±（τ） on the state ｜q, 0）, is ...In this paper a new class of finite-dimensional even and odd nonlinear pair coherent states （EONLPCSs）, which can be realized via operating the superposed evolution operators D±（τ） on the state ｜q, 0）, is constructed, then their orthonormalized property, completeness relations and some nonclassical properties are discussed. It is shown that the finite-dimensional EONLPCSs possess normalization and completeness relations. Moreover, the finite-dimensional EONLPCSs exhibit remarkably different sub-Poissonian distributions and phase probability distributions for different values of parameters q, η and ξ.展开更多
Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified r-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the...Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified r-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the concept and representations of modified RotaBaxter Hom-Lie algebras. We develop a cohomology of modified Rota-Baxter Hom-Lie algebras with coefficients in a suitable representation. As applications, we study formal deformations and abelian extensions of modified Rota-Baxter Hom-Lie algebras in terms of second cohomology groups.展开更多
In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests mo...In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests modulo this biideal.As an application,a connected graded bialgebra and so a graded Hopf algebra on matching Rota-Baxter algebras are constructed,which simplifies the Hopf algebraic structure proposed by[Pacific J.Math.,2022,317(2):441-475].展开更多
The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce t...The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce the representation of modifiedλ-differential Lie-Yamaguti algebras.Furthermore,we establish the cohomology of a modifiedλ-differential Lie-Yamaguti algebra with coefficients in a representation.Finally,we investigate the one-parameter formal deformations and Abelian extensions of modifiedλ-differential Lie-Yamaguti algebras using the second cohomology group.展开更多
Let D(n)be the finite dimensional non-pointed and non-semisimple Hopf algebra,which is a quotient of a prime Hopf algebras of GK-dimension one for an odd number n>1.In this paper,we investigate the structure of Yet...Let D(n)be the finite dimensional non-pointed and non-semisimple Hopf algebra,which is a quotient of a prime Hopf algebras of GK-dimension one for an odd number n>1.In this paper,we investigate the structure of Yetter-Drinfeld simple modules over D(n)and give iso-classes of them.展开更多
A left Leibniz algebra equipped with an invariant nondegenerate skew-symmetric bilinear form(i.e.,a skew-symmetric quadratic Leibniz algebra)is constructed.The notion of T^(*)-extension of Lie-Yamaguti algebras is int...A left Leibniz algebra equipped with an invariant nondegenerate skew-symmetric bilinear form(i.e.,a skew-symmetric quadratic Leibniz algebra)is constructed.The notion of T^(*)-extension of Lie-Yamaguti algebras is introduced and it is observed that the trivial extension of a Lie-Yamaguti algebra is a quadratic Lie-Yamaguti algebra.It is proved that every symmetric(resp.,skew-symmetric)quadratic Leibniz algebra induces a quadratic(resp.,symplectic)LieYamaguti algebra.展开更多
基金Sponsored by the Scientific Research Fund of Heilongjiang Provincial Education Department (11541109)the Science Foundation of Harbin Normal University (KM2007-11)
文摘The filtration structure of finite-dimensional special odd Hamilton superalgebras over a field of prime characteristic was studied. By determining ad-nilpotent dements in the even part, the natural filtration of special odd Hamiltonian superalgebras is proved to be invariant. Using this result, the special odd Hamilton superalgebras is classified. Finally, the automorphism group of the restricted special odd Hamilton superalgebras is determined.
基金Supported by the National Natural Science Foundation of China（Ill01084） Supported by the Fujian Province Natural Science Foundation of China
文摘A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapφon P is commuting if and only if φ is a scalar multiplication map on P.
文摘In the paper we will give a complete classification of finite-dimemsional simple Novikov algebras over an algebraically closed field with prime characteristic p>2.
基金The second author thanks FAPESP(processo 2018/11292-6)of Brazil,and the Ministry of EducationScience of the Russian Federation within the scope of the base part of a State Assignment within the sphere of scientific activity(Project No.2.9314.2017)for financial supportThe third author thanks SNI and FAPESP grant process 2015/07245-4 for support.
文摘We study the variety of binary Lie algebras defined by the identities x^(2)=J(x,y,zu)=0,where J(a,b,c)denotes the Jacobian of a,b,c.Building on previous work by Carrillo,Rasskazova,Sabinina and Grishkov,in the present article it is shown that the Levi and Malcev theorems hold for this variety of algebras.
文摘The fact that infinite-dimensional algebra exists in a 2-dimensional Lax-pair system has caused keen interest.Using a variety of particular models, many explicit expressions have already been derived. Since the hidden symmetry algebra was introduced in principal chiral model, the study of axially symmetric gravity with
基金Supported by the Science and Technology Program of Guizhou Province(Grant No.QKHJC QN[2025]362)the National Natural Science Foundation of China(Grant No.12361005).
文摘Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algebras and tri-associative algebras.We introduce the notion of a quad-dendriform algebra,which is a splitting of a di-associative algebra.We show that a relative averaging operator on dendriform algebras gives rise to a quad-dendriform algebra.Furthermore,we introduce the notion of six-dendriform algebras,which are splittings of the tri-associative algebras,and demonstrate that homomorphic relative averaging operators induce six-dendriform algebras.
基金National Natural Science Foundation of China(11971315)。
文摘Lie algebras are special Leibniz algebras,so it is natural to view Lie algebras as Leibniz algebras.In this paper,we calculate all the Leibniz 2 cocycles of the Lie algebra K(1,0),which is helpful to classify one dimensional central extensions of K(1,0)as Leibniz algebra.
基金supported in part by the National Natural Science Foundation of China under Grants 62073124 and U1804150.
文摘This paper explores the algebraic essence of universal logic functions(ULFs)from an algebraic perspective.Under the framework of semi-tensor product of matrices,the“sequential nature”of ULFs is revealed.Utilizing the nature,a technique called universal transformation method is proposed,by which any ULF can be transformed into an equivalent expression with desired features that facilitate achieving specific objectives,such as modeling,analyzing and synthesizing universal logical systems.Furthermore,several useful logical operators are constructed in a mixed-dimensional situation,including power-raising operator,power-descending operator,erasure operator,and appending operator.Finally,these results are applied to model and analyze finite state machines and their networks,which demonstrate the practical value of the method and operators.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61332019,61671287,and 61631014)the National Key Research and Development Program of China(Grant No.2016YFA0302600)
文摘The well-known multi-dimensional reconciliation is an effective method used in the continuous-variable quantum key distribution in the long-distance and the low signal-to-noise-ratio scenarios.The virtual channel employed to exchange data is generally established by using a finite-dimensional rotation in the reconciliation procedure.In this paper,we found that the finite dimension of the multi-dimensional reconciliation inevitably leads to the mismatch of the signal-to-noise-ratio between the quantum channel and the virtual channel,which may be called the finite-dimension effect.Such an effect results in an overestimation on the secret key rate,and subsequently induces vital practical security loopholes.
基金Project supported by the National Natural Science Foundation of China(No.11071158)Shanghai Leading Academic Discipline Project(No.S30104)
文摘A new concept of convergence （R-convergence） of a sequence of measures is applied to characterize global minimizers in a functional space as a sequence of approximate solutions in finite-dimensional spaces. A deviation integral approach is used to find such solutions. For a constrained problem, a penalized deviation integral algorithm is proposed to convert it to unconstrained ones. A numerical example on an optimal control problem with non-convex state constraints is given to show the effectiveness of the algorithm.
文摘We theoretically analyze the photon number distribution,entanglement entropy,and Wigner phase-space distribution,considering the finite-dimensional pair coherent state(FDPCS)generated in the nonlinear Bose operator realization.Our results show that the photon number distribution is governed by the two-mode photon number sum q of the FDPCS,the entanglement of the FDPCS always increases quickly at first and then decreases slowly for any q,and the nonclassicality of the FDPCS for odd q is more stronger than that for even q.
文摘This paper discusses the properties of amplitude-squared squeezing of the generalized odd-even coherent states of anharmonic oscillator in finite-dimensional Hilbert space. It demonstrates that the generalized odd coherent states do exhibit strong amplitude-squared squeezing effects in comparison with the generalized even coherent states.
文摘In this paper, we demonstrate that the finite-dimensional approximations to the solutions of a linear bond-based peridynamic boundary value problem converge to the exact solution exponentially with the analyticity assumption of the forcing term, therefore greatly improve the convergence rate derived in literature.
基金Project supported by the National Natural Science Foundation of China(Grant No.10574060)the Natural Science Foundation of Shandong Province,China(Grant No.Y2008A23and ZR2010AQ027)the Shandong Province Higher Educational Science and Technology Program,China(Grant Nos.J09LA07and J10LA15).
文摘This paper constructs a new type of finite-dimensional thermal coherent states （FDTCS）, which differs from the proceeding thermal coherent state in construction, as realisations of SU（2） Lie algebra. Using the technique of integration within an ordered product of operator, it investigates the orthonormality and completeness relation of the FDTCS. Based on the thermal Wigner operator in the thermal entangled state representation, the Wigner function of the FDTCS is obtained. The nonclassical properties of the FDTCS are discussed in terms of the negativity of its Wigner function.
基金supported by the National Natural Science Foundation of China (Grant 10574060)the Natural Science Foundation of Liaocheng University of China (Grant No X071049)
文摘In this paper a new class of finite-dimensional even and odd nonlinear pair coherent states （EONLPCSs）, which can be realized via operating the superposed evolution operators D±（τ） on the state ｜q, 0）, is constructed, then their orthonormalized property, completeness relations and some nonclassical properties are discussed. It is shown that the finite-dimensional EONLPCSs possess normalization and completeness relations. Moreover, the finite-dimensional EONLPCSs exhibit remarkably different sub-Poissonian distributions and phase probability distributions for different values of parameters q, η and ξ.
基金Supported by the Universities Key Laboratory of System Modeling and Data Mining in Guizhou Province(Grant No.2023013)the National Natural Science Foundation of China(Grant No.12161013)the Science and Technology Program of Guizhou Province(Grant No.ZK[2023]025)。
文摘Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified r-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the concept and representations of modified RotaBaxter Hom-Lie algebras. We develop a cohomology of modified Rota-Baxter Hom-Lie algebras with coefficients in a suitable representation. As applications, we study formal deformations and abelian extensions of modified Rota-Baxter Hom-Lie algebras in terms of second cohomology groups.
基金Supported by NSFC(No.12101316)Belt and Road Innovative Talents Exchange Foreign Experts project(No.DL2023014002L)。
文摘In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests modulo this biideal.As an application,a connected graded bialgebra and so a graded Hopf algebra on matching Rota-Baxter algebras are constructed,which simplifies the Hopf algebraic structure proposed by[Pacific J.Math.,2022,317(2):441-475].
基金National Natural Science Foundation of China(12161013)Research Projects of Guizhou University of Commerce in 2024。
文摘The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce the representation of modifiedλ-differential Lie-Yamaguti algebras.Furthermore,we establish the cohomology of a modifiedλ-differential Lie-Yamaguti algebra with coefficients in a representation.Finally,we investigate the one-parameter formal deformations and Abelian extensions of modifiedλ-differential Lie-Yamaguti algebras using the second cohomology group.
基金Supported by the Fundamental Research Program of Shanxi Province(Grant No.202303021212147)the National Natural Science Foundation of China(Grant No.12471038)。
文摘Let D(n)be the finite dimensional non-pointed and non-semisimple Hopf algebra,which is a quotient of a prime Hopf algebras of GK-dimension one for an odd number n>1.In this paper,we investigate the structure of Yetter-Drinfeld simple modules over D(n)and give iso-classes of them.
文摘A left Leibniz algebra equipped with an invariant nondegenerate skew-symmetric bilinear form(i.e.,a skew-symmetric quadratic Leibniz algebra)is constructed.The notion of T^(*)-extension of Lie-Yamaguti algebras is introduced and it is observed that the trivial extension of a Lie-Yamaguti algebra is a quadratic Lie-Yamaguti algebra.It is proved that every symmetric(resp.,skew-symmetric)quadratic Leibniz algebra induces a quadratic(resp.,symplectic)LieYamaguti algebra.
