本文刻画*代数上完全保混合Lie零积的非线性映射,利用该结论得到不含交换中心投影的von Neumann代数上*-同构的等价刻画。In this paper, we characterize nonlinear maps on *-algebras completely preserving mixed Lie zero products...本文刻画*代数上完全保混合Lie零积的非线性映射,利用该结论得到不含交换中心投影的von Neumann代数上*-同构的等价刻画。In this paper, we characterize nonlinear maps on *-algebras completely preserving mixed Lie zero products. As its application, equivalent characterization of *-isomorphism on von Neumann algebra with no abelian center projections is obtained.展开更多
Let R be a commutative ring with unity and T be a triangular algebra over R.Let a sequence G={G_n}_(n∈N)of nonlinear mappings G_n:T→T associated with nonlinear Lie triple higher derivations∆={δ_n}_(n∈N)by local ac...Let R be a commutative ring with unity and T be a triangular algebra over R.Let a sequence G={G_n}_(n∈N)of nonlinear mappings G_n:T→T associated with nonlinear Lie triple higher derivations∆={δ_n}_(n∈N)by local actions be a generalized Lie triple higher derivation by local actions satisfying Gn([[x,y],z])=Σ_(i+j+k=n)[[Gi(x),δj(y)],δk(z)]for all x,y,z∈T with xyz=0.Under some mild conditions on T,we prove in this paper that every nonlinear generalized Lie triple higher derivation by local actions on triangular algebras is proper.As an application we shall give a characterization of nonlinear generalized Lie triple higher derivations by local actions on upper triangular matrix algebras and nest algebras,respectively.At the same time,it also improves some interesting conclusions,such as[J.Algebra Appl.22(3),2023,Paper No.2350059],[Axioms,11,2022,1–16].展开更多
设ℳ和N是无I1或I2型中心直和项的von Neumann代数,其单位元分别为I和I′。本文证明非线性双射Φ:ℳ→N混合Lie可乘,即Φ([ [ A,B ],C ]∗)=[ [ Φ(A),Φ(B) ],Φ(C) ]∗,∀A,B,C∈ℳ,当且仅当存在线性*-同构和共轭线性*-同构的直和Ψ:ℳ→N使...设ℳ和N是无I1或I2型中心直和项的von Neumann代数,其单位元分别为I和I′。本文证明非线性双射Φ:ℳ→N混合Lie可乘,即Φ([ [ A,B ],C ]∗)=[ [ Φ(A),Φ(B) ],Φ(C) ]∗,∀A,B,C∈ℳ,当且仅当存在线性*-同构和共轭线性*-同构的直和Ψ:ℳ→N使得Φ(A)=Φ(I)Ψ(A),∀A∈ℳ,其中Φ(I)∈N是可逆中心元且Φ(I)2=I′。该结论将因子von Neumann代数上的非线性混合Lie可乘双射的结果推广到无I1或I2型中心直和项的von Neumann代数。Let ℳand Nbe von Neumann algebras with no central summands of type I1or I2, Iand I′be the identities of them. This paper proves that a bijective map Φ:ℳ→Nis mixed Lie multiplicative, that is, Φ([ [ A,B ],C ]∗)=[ [ Φ(A),Φ(B) ],Φ(C) ]∗,∀A,B,C∈ℳif and only if Φ(A)=Φ(I)Ψ(A)for all A∈ℳ, where Ψ:ℳ→Nis a direct sum of a linear *-isomorphism and a conjugate linear *-isomorphism, Φ(I)is a central element in Nwith Φ(I)2=I′. The results about mixed Lie multiplicative maps on factor von Neumann algebras are generalized to von Neumann algebras with no central summands of type I1or I2.展开更多
Lying in politics has long been seen as both routine and destructive.While some falsehoods appear trivial,others undermine democratic processes,erode trust,and inflict significant harm on society.This essay investigat...Lying in politics has long been seen as both routine and destructive.While some falsehoods appear trivial,others undermine democratic processes,erode trust,and inflict significant harm on society.This essay investigates the moral,legal,and political dimensions of punishing political lies,drawing on Kantian deontological ethics,consequentialist reasoning,and theories of democratic communication.It distinguishes minor misstatements from harmful falsehoods that distort elections,public health responses,and national security.Building on Hannah Arendt’s warning about the collapse of truth and Jürgen Habermas’s emphasis on communicative integrity,the analysis shows how unchecked deception corrodes the foundations of democratic legitimacy.Although legal punishment risks overreach and potential misuse,political and social sanctions remain essential tools of accountability.By examining cases such as misinformation in the Iraq War and the COVID-19 pandemic,the essay argues that meaningful consequences for harmful lies are indispensable to maintaining truth as a shared democratic norm.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
In this paper,the Lie symmetry analysis method is applied to the(2+1)-dimensional time-fractional Heisenberg ferromagnetic spin chain equation.We obtain all the Lie symmetries admitted by the governing equation and re...In this paper,the Lie symmetry analysis method is applied to the(2+1)-dimensional time-fractional Heisenberg ferromagnetic spin chain equation.We obtain all the Lie symmetries admitted by the governing equation and reduce the corresponding(2+1)-dimensional fractional partial differential equations with the Riemann–Liouville fractional derivative to(1+1)-dimensional counterparts with the Erdélyi–Kober fractional derivative.Then,we obtain the power series solutions of the reduced equations,prove their convergence and analyze their dynamic behavior graphically.In addition,the conservation laws for all the obtained Lie symmetries are constructed using the new conservation theorem and the generalization of Noether operators.展开更多
In this paper,we study the Hom-structures of a special class of solvable Lie algebras with naturally graded filiform nilradical n_(n,1).Over an algebraically closed field F of zero characteristic,we calculate the Hom-...In this paper,we study the Hom-structures of a special class of solvable Lie algebras with naturally graded filiform nilradical n_(n,1).Over an algebraically closed field F of zero characteristic,we calculate the Hom-structures of these solvable Lie algebras using the Hom-Jacobi identity,obtain the bases of these Hom-structures and observe that there are certain similarities among these bases.展开更多
In the present article, the authors give some properties on subinvariant subalgebras of modular Lie superalgebras and obtain the derivation tower theorem of modular Lie superalgebras, which is analogous to the automor...In the present article, the authors give some properties on subinvariant subalgebras of modular Lie superalgebras and obtain the derivation tower theorem of modular Lie superalgebras, which is analogous to the automorphism tower theorem of finite groups. Moreover, they announce and prove some results of modular complete Lie superalgebras.展开更多
A compatible Lie algebra is a pair of Lie algebras such that any linear combination of the two Lie brackets is a Lie bracket. We construct a bialgebra theory of compatible Lie Mgebras as an analogue of a piiLie bialge...A compatible Lie algebra is a pair of Lie algebras such that any linear combination of the two Lie brackets is a Lie bracket. We construct a bialgebra theory of compatible Lie Mgebras as an analogue of a piiLie bialgebra. They can also be regarded as a ＂compatible version＂ of Lie bialgebras, that is, a pair of Lie biaJgebras such that any linear combination of the two Lie bialgebras is still a Lie bialgebra. Many properties of compatible Lie bialgebras as the ＂compatible version＂ of the corresponding properties of Lie biaJgebras are presented. In particular, there is a coboundary compatible Lie bialgebra theory with a construction from the classical Yang-Baxter equation in compatible Lie algebras as a combination of two classical Yang-Baxter equations in lAe algebras. FUrthermore, a notion of compatible pre-Lie Mgebra is introduced with an interpretation of its close relation with the classical Yang-Baxter equation in compatible Lie a/gebras which leads to a construction of the solutions of the latter. As a byproduct, the compatible Lie bialgebras fit into the framework to construct non-constant solutions of the classical Yang-Baxter equation given by Golubchik and Sokolov.展开更多
文摘本文刻画*代数上完全保混合Lie零积的非线性映射,利用该结论得到不含交换中心投影的von Neumann代数上*-同构的等价刻画。In this paper, we characterize nonlinear maps on *-algebras completely preserving mixed Lie zero products. As its application, equivalent characterization of *-isomorphism on von Neumann algebra with no abelian center projections is obtained.
基金Supported by Open Research Fund of Hubei Key Laboratory of Mathematical Sciences(Central China Normal University)the Natural Science Foundation of Anhui Province(Grant No.2008085QA01)the University Natural Science Research Project of Anhui Province(Grant No.KJ2019A0107)。
文摘Let R be a commutative ring with unity and T be a triangular algebra over R.Let a sequence G={G_n}_(n∈N)of nonlinear mappings G_n:T→T associated with nonlinear Lie triple higher derivations∆={δ_n}_(n∈N)by local actions be a generalized Lie triple higher derivation by local actions satisfying Gn([[x,y],z])=Σ_(i+j+k=n)[[Gi(x),δj(y)],δk(z)]for all x,y,z∈T with xyz=0.Under some mild conditions on T,we prove in this paper that every nonlinear generalized Lie triple higher derivation by local actions on triangular algebras is proper.As an application we shall give a characterization of nonlinear generalized Lie triple higher derivations by local actions on upper triangular matrix algebras and nest algebras,respectively.At the same time,it also improves some interesting conclusions,such as[J.Algebra Appl.22(3),2023,Paper No.2350059],[Axioms,11,2022,1–16].
文摘设ℳ和N是无I1或I2型中心直和项的von Neumann代数,其单位元分别为I和I′。本文证明非线性双射Φ:ℳ→N混合Lie可乘,即Φ([ [ A,B ],C ]∗)=[ [ Φ(A),Φ(B) ],Φ(C) ]∗,∀A,B,C∈ℳ,当且仅当存在线性*-同构和共轭线性*-同构的直和Ψ:ℳ→N使得Φ(A)=Φ(I)Ψ(A),∀A∈ℳ,其中Φ(I)∈N是可逆中心元且Φ(I)2=I′。该结论将因子von Neumann代数上的非线性混合Lie可乘双射的结果推广到无I1或I2型中心直和项的von Neumann代数。Let ℳand Nbe von Neumann algebras with no central summands of type I1or I2, Iand I′be the identities of them. This paper proves that a bijective map Φ:ℳ→Nis mixed Lie multiplicative, that is, Φ([ [ A,B ],C ]∗)=[ [ Φ(A),Φ(B) ],Φ(C) ]∗,∀A,B,C∈ℳif and only if Φ(A)=Φ(I)Ψ(A)for all A∈ℳ, where Ψ:ℳ→Nis a direct sum of a linear *-isomorphism and a conjugate linear *-isomorphism, Φ(I)is a central element in Nwith Φ(I)2=I′. The results about mixed Lie multiplicative maps on factor von Neumann algebras are generalized to von Neumann algebras with no central summands of type I1or I2.
文摘Lying in politics has long been seen as both routine and destructive.While some falsehoods appear trivial,others undermine democratic processes,erode trust,and inflict significant harm on society.This essay investigates the moral,legal,and political dimensions of punishing political lies,drawing on Kantian deontological ethics,consequentialist reasoning,and theories of democratic communication.It distinguishes minor misstatements from harmful falsehoods that distort elections,public health responses,and national security.Building on Hannah Arendt’s warning about the collapse of truth and Jürgen Habermas’s emphasis on communicative integrity,the analysis shows how unchecked deception corrodes the foundations of democratic legitimacy.Although legal punishment risks overreach and potential misuse,political and social sanctions remain essential tools of accountability.By examining cases such as misinformation in the Iraq War and the COVID-19 pandemic,the essay argues that meaningful consequences for harmful lies are indispensable to maintaining truth as a shared democratic norm.
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 State Key Program of the National Natural Science Foundation of China(72031009).
文摘In this paper,the Lie symmetry analysis method is applied to the(2+1)-dimensional time-fractional Heisenberg ferromagnetic spin chain equation.We obtain all the Lie symmetries admitted by the governing equation and reduce the corresponding(2+1)-dimensional fractional partial differential equations with the Riemann–Liouville fractional derivative to(1+1)-dimensional counterparts with the Erdélyi–Kober fractional derivative.Then,we obtain the power series solutions of the reduced equations,prove their convergence and analyze their dynamic behavior graphically.In addition,the conservation laws for all the obtained Lie symmetries are constructed using the new conservation theorem and the generalization of Noether operators.
基金Supported by National Natural Science Foundation of China(12271085)Supported by National Natural Science Foundation of Heilongjiang Province(LH2022A019)+3 种基金Basic Scientic Research Operating Funds for Provincial Universities in Heilongjiang Province(2020 KYYWF 1018)Heilongjiang University Outstanding Youth Science Foundation(JCL202103)Heilongjiang University Educational and Teaching Reform Research Project(2024C43)Heilongjiang University Postgraduate Education Reform Project(JGXM_YJS_2024010).
文摘In this paper,we study the Hom-structures of a special class of solvable Lie algebras with naturally graded filiform nilradical n_(n,1).Over an algebraically closed field F of zero characteristic,we calculate the Hom-structures of these solvable Lie algebras using the Hom-Jacobi identity,obtain the bases of these Hom-structures and observe that there are certain similarities among these bases.
基金Supported by Youth Science Foundation of Northeast Normal University (111494027) National Natural Science Foundation of China (10271076)
文摘In the present article, the authors give some properties on subinvariant subalgebras of modular Lie superalgebras and obtain the derivation tower theorem of modular Lie superalgebras, which is analogous to the automorphism tower theorem of finite groups. Moreover, they announce and prove some results of modular complete Lie superalgebras.
基金Supported by National Natural Science Foundation of China under Grant Nos.11271202,11221091,11425104Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20120031110022
文摘A compatible Lie algebra is a pair of Lie algebras such that any linear combination of the two Lie brackets is a Lie bracket. We construct a bialgebra theory of compatible Lie Mgebras as an analogue of a piiLie bialgebra. They can also be regarded as a ＂compatible version＂ of Lie bialgebras, that is, a pair of Lie biaJgebras such that any linear combination of the two Lie bialgebras is still a Lie bialgebra. Many properties of compatible Lie bialgebras as the ＂compatible version＂ of the corresponding properties of Lie biaJgebras are presented. In particular, there is a coboundary compatible Lie bialgebra theory with a construction from the classical Yang-Baxter equation in compatible Lie algebras as a combination of two classical Yang-Baxter equations in lAe algebras. FUrthermore, a notion of compatible pre-Lie Mgebra is introduced with an interpretation of its close relation with the classical Yang-Baxter equation in compatible Lie a/gebras which leads to a construction of the solutions of the latter. As a byproduct, the compatible Lie bialgebras fit into the framework to construct non-constant solutions of the classical Yang-Baxter equation given by Golubchik and Sokolov.
