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
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
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
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
This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along wit...This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along with an exploration of their properties.Moreover,we investigate the structure of triangle bounded L⁃algebra with a special condition.Secondly,we define the concept of triangle ideals of triangle bounded L⁃algebra and explore the connection between the triangle ideals of triangle bounded L⁃algebra L and the ideals of bounded L⁃algebra E(L).In addition,we classified and studied various classes of triangle ideals,including Stonean triangle ideals,extended Stonean triangle ideals,and lattice ideals,and by introducing the notion of Stonean triangle bounded L algebras,we examine the relationship between Stonean triangle bounded L⁃algebras and Stonean triangle ideals.Finally,we investigate the interrelationships among these various types of triangle ideals.展开更多
In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family...In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family of vertex operator algebras V_(√kA_(1)) associated to rank-one positive definite even lattices √kA_(1) for arbitrary positive integers k to characterize these even lattice vertex operator algebras.In such a family of lattice vertex operator algebras V_(√kA_(1)),the vertex operator algebra V_(√2A_(1)) is different from others.Hence we describe the varieties of semi-conformal vectors of V_(√2A_(1)) and the fixed vertex operator subalgebra V^(+)√2A_(1).Moreover,as applications,we study the relations between vertex operator algebras V_(√kA_(1) )and L_(sl_(2))(k,0)for arbitrary positive integers k by the viewpoint of semi-conformal homomorphisms of vertex operator algebras.For case k=2,in the series of rational simple affine vertex operator algebras L_(sl_(2))(k,0)for positive integers k,we show that L_(sl_(2))(2,0)is a unique frame vertex operator algebra with rank 3.展开更多
In this paper,we first introduce the notion of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras and define a cohomology of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras w...In this paper,we first introduce the notion of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras and define a cohomology of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras with coefficients in a suitable representation.Next,we introduce and study 3-Hom-post-Lie-algebras as the underlying structure of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras.Finally,we investigate relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras induced by Hom-Lie algebras.展开更多
In this paper,we introduce non-abelian cohomology groups and classify the nonabelian extensions of Rota-Baxter pre-Lie algebras in terms of non-abelian cohomology groups.Next,we explore the inducibility of pairs of au...In this paper,we introduce non-abelian cohomology groups and classify the nonabelian extensions of Rota-Baxter pre-Lie algebras in terms of non-abelian cohomology groups.Next,we explore the inducibility of pairs of automorphisms and derive the analog Wells exact sequences under the circumstance of Rota-Baxter pre-Lie algebras.Finally,we discuss the inducibility problem of pairs of automorphisms about an abelian extensions of Rota-Baxter pre-Lie algebras.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
Let T,U be two Artin algebras and_(U)M_(T)be a U-T-bimodule.In this paper,we get a necessary and sufficient condition such that the formal triangular matrix algebra Λ=(T 0 M U)is(m,n)-Igusa-Todorov when_(U)M,M_(T)are...Let T,U be two Artin algebras and_(U)M_(T)be a U-T-bimodule.In this paper,we get a necessary and sufficient condition such that the formal triangular matrix algebra Λ=(T 0 M U)is(m,n)-Igusa-Todorov when_(U)M,M_(T)are projective.We also study the Igusa-Todorov dimension of Λ.More specifically,it is proved that max{IT.dim T,IT.dim U}≤IT.dim Λ≤min{max{gl.dim T,IT.dim U},max{gl.dim U,IT.dim T}}.展开更多
In this paper,we consider Lie conformal algebras with derivations.A pair consisting of a Lie conformal algebra and a distinguished derivation is called a LieCDer pair.We introduce a cohomology theory for LieCDer pair ...In this paper,we consider Lie conformal algebras with derivations.A pair consisting of a Lie conformal algebra and a distinguished derivation is called a LieCDer pair.We introduce a cohomology theory for LieCDer pair with coefficients in a representation.Furthermore,we study abelian extensions of a LieCDer pair as an application of cohomology theory.Finally,we consider homotopy derivations on 2-term conformal L_(∞)-algebras and 2-derivations on conformal Lie 2-algebras.The category of 2-term conformal L_(∞)-algebras with homotopy derivations is equivalent to the category of conformal Lie 2-algebras with 2-derivations.展开更多
In this paper,X is a locally compact Hausdorff space and A is a Banach algebra.First,we study some basic features of C0(X,A)related to BSE concept,which are gotten from A.In particular,we prove that if C0(X,A)has the ...In this paper,X is a locally compact Hausdorff space and A is a Banach algebra.First,we study some basic features of C0(X,A)related to BSE concept,which are gotten from A.In particular,we prove that if C0(X,A)has the BSE property then A has so.We also establish the converse of this result,whenever X is discrete and A has the BSE-norm property.Furthermore,we prove the same result for the BSE property of type I.Finally,we prove that C0(X,A)has the BSE-norm property if and only if A has so.展开更多
In this paper,we define the cohomology of a Reynolds Leibniz algebra with coefficients in a suitable representation.We also introduce the notion of Reynolds Leibniz 2-algebras,and prove that strict Reynolds Leibniz 2-...In this paper,we define the cohomology of a Reynolds Leibniz algebra with coefficients in a suitable representation.We also introduce the notion of Reynolds Leibniz 2-algebras,and prove that strict Reynolds Leibniz 2-algebras are equivalent to crossed modules of Reynolds Leibniz algebras.展开更多
In this paper,we give an explicit and systematic study on the double constructions of Frobenius Hom-algebras and introduce the close relations between O-operators and Homdendriform algebras.Furthermore,we study the do...In this paper,we give an explicit and systematic study on the double constructions of Frobenius Hom-algebras and introduce the close relations between O-operators and Homdendriform algebras.Furthermore,we study the double constructions of Connes cocycles in terms of Hom-dendriform algebras.Finally,we give a clear analogy between antisymmetric infinitesimal Hom-bialgebras and Hom-dendriform D-bialgebras.展开更多
In this paper,we introduce the notion of embedding tensors on 3-Hom-Lie algebras and show that embedding tensors induce naturally 3-Hom-Leibniz algebras.Moreover,the cohomology theory of embedding tensors on 3-Hom-Lie...In this paper,we introduce the notion of embedding tensors on 3-Hom-Lie algebras and show that embedding tensors induce naturally 3-Hom-Leibniz algebras.Moreover,the cohomology theory of embedding tensors on 3-Hom-Lie algebras is defined.As an application,we show that if two linear deformations of an embedding tensor on a 3-Hom-Lie algebra are equivalent,then their infinitesimals belong to the same cohomology class in the first cohomology group.展开更多
Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F -algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to...Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F -algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to be an algebraically closed field of characteristic zero, K a finite group, F K the group algebra of K over F , then all local automorphisms of F K are also characterized.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
Some relationships between the representation of Hom-Jacobi-Jordan algebra and that of Jacobi-Jordan algebra are studied.Moreover,by using the notion ofαk-anti-derivation,a property theorem of multiplicative Hom-Jaco...Some relationships between the representation of Hom-Jacobi-Jordan algebra and that of Jacobi-Jordan algebra are studied.Moreover,by using the notion ofαk-anti-derivation,a property theorem of multiplicative Hom-Jacobi-Jordan algebras is also given.展开更多
In this paper,we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent,respectively,and then,as applications,we obta...In this paper,we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent,respectively,and then,as applications,we obtain the concrete characterizations of all nonadditive skew(anti-)commuting maps on some operator algebras.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
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 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.
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.
基金Sponsored by Foreign Expert Program of China(Grant No.DL2023041002L)Yulin City Industry University Research Project(Grant No.CXY-2022-59).
文摘This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along with an exploration of their properties.Moreover,we investigate the structure of triangle bounded L⁃algebra with a special condition.Secondly,we define the concept of triangle ideals of triangle bounded L⁃algebra and explore the connection between the triangle ideals of triangle bounded L⁃algebra L and the ideals of bounded L⁃algebra E(L).In addition,we classified and studied various classes of triangle ideals,including Stonean triangle ideals,extended Stonean triangle ideals,and lattice ideals,and by introducing the notion of Stonean triangle bounded L algebras,we examine the relationship between Stonean triangle bounded L⁃algebras and Stonean triangle ideals.Finally,we investigate the interrelationships among these various types of triangle ideals.
基金Supported by National Natural Science Foundation of China(Grant No.12475002).
文摘In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family of vertex operator algebras V_(√kA_(1)) associated to rank-one positive definite even lattices √kA_(1) for arbitrary positive integers k to characterize these even lattice vertex operator algebras.In such a family of lattice vertex operator algebras V_(√kA_(1)),the vertex operator algebra V_(√2A_(1)) is different from others.Hence we describe the varieties of semi-conformal vectors of V_(√2A_(1)) and the fixed vertex operator subalgebra V^(+)√2A_(1).Moreover,as applications,we study the relations between vertex operator algebras V_(√kA_(1) )and L_(sl_(2))(k,0)for arbitrary positive integers k by the viewpoint of semi-conformal homomorphisms of vertex operator algebras.For case k=2,in the series of rational simple affine vertex operator algebras L_(sl_(2))(k,0)for positive integers k,we show that L_(sl_(2))(2,0)is a unique frame vertex operator algebra with rank 3.
基金Supported by the National Natural Science Foundation of China(Grant No.12161013)the School-Level Student Research Project of Guizhou University of Finance and Economics(Grant No.2024ZXSY231)。
文摘In this paper,we first introduce the notion of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras and define a cohomology of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras with coefficients in a suitable representation.Next,we introduce and study 3-Hom-post-Lie-algebras as the underlying structure of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras.Finally,we investigate relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras induced by Hom-Lie algebras.
基金Supported by the National Natural Science Foundation of China(Grant No.12161013)the School-Level Student Research Project of Guizhou University of Finance and Economics(Grant No.2024ZXSY239).
文摘In this paper,we introduce non-abelian cohomology groups and classify the nonabelian extensions of Rota-Baxter pre-Lie algebras in terms of non-abelian cohomology groups.Next,we explore the inducibility of pairs of automorphisms and derive the analog Wells exact sequences under the circumstance of Rota-Baxter pre-Lie algebras.Finally,we discuss the inducibility problem of pairs of automorphisms about an abelian extensions of Rota-Baxter pre-Lie algebras.
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].
基金Supported by the National Natural Science Foundation of China(Grant No.12301041)the Science Foundation for Distinguished Young Scholars of Anhui Province(Grant No.2108085J01)。
文摘Let T,U be two Artin algebras and_(U)M_(T)be a U-T-bimodule.In this paper,we get a necessary and sufficient condition such that the formal triangular matrix algebra Λ=(T 0 M U)is(m,n)-Igusa-Todorov when_(U)M,M_(T)are projective.We also study the Igusa-Todorov dimension of Λ.More specifically,it is proved that max{IT.dim T,IT.dim U}≤IT.dim Λ≤min{max{gl.dim T,IT.dim U},max{gl.dim U,IT.dim T}}.
基金Supported by the National Natural Science Foundation of China(Grant No.12161013)the Basic Research Program(Natural Science)of Guizhou Province(Grant No.ZK[2023]025)。
文摘In this paper,we consider Lie conformal algebras with derivations.A pair consisting of a Lie conformal algebra and a distinguished derivation is called a LieCDer pair.We introduce a cohomology theory for LieCDer pair with coefficients in a representation.Furthermore,we study abelian extensions of a LieCDer pair as an application of cohomology theory.Finally,we consider homotopy derivations on 2-term conformal L_(∞)-algebras and 2-derivations on conformal Lie 2-algebras.The category of 2-term conformal L_(∞)-algebras with homotopy derivations is equivalent to the category of conformal Lie 2-algebras with 2-derivations.
文摘In this paper,X is a locally compact Hausdorff space and A is a Banach algebra.First,we study some basic features of C0(X,A)related to BSE concept,which are gotten from A.In particular,we prove that if C0(X,A)has the BSE property then A has so.We also establish the converse of this result,whenever X is discrete and A has the BSE-norm property.Furthermore,we prove the same result for the BSE property of type I.Finally,we prove that C0(X,A)has the BSE-norm property if and only if A has so.
基金Supported by the National Natural Science Foundation of China(Grant No.12271292)。
文摘In this paper,we define the cohomology of a Reynolds Leibniz algebra with coefficients in a suitable representation.We also introduce the notion of Reynolds Leibniz 2-algebras,and prove that strict Reynolds Leibniz 2-algebras are equivalent to crossed modules of Reynolds Leibniz algebras.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11761017,11801150)the Science and Technology Foundation of Guizhou Province(Grant No.20201Y005)。
文摘In this paper,we give an explicit and systematic study on the double constructions of Frobenius Hom-algebras and introduce the close relations between O-operators and Homdendriform algebras.Furthermore,we study the double constructions of Connes cocycles in terms of Hom-dendriform algebras.Finally,we give a clear analogy between antisymmetric infinitesimal Hom-bialgebras and Hom-dendriform D-bialgebras.
基金Supported by the Scientific Research Foundation for Science&Technology Innovation Talent Team of the Intelligent Computing and Monitoring of Guizhou Province(Grant No.QJJ[2023]063)the Science and Technology Program of Guizhou Province(Grant Nos.ZK[2023]025+4 种基金QKHZC[2023]372ZK[2022]031)the National Natural Science Foundation of China(Grant No.12161013)the Scientific Research Foundation of Guizhou University of Finance and Economics(Grant No.2022KYYB08)the Doctoral Research Start-Up Fund of Guiyang University(Grant No.GYU-KY-2024).
文摘In this paper,we introduce the notion of embedding tensors on 3-Hom-Lie algebras and show that embedding tensors induce naturally 3-Hom-Leibniz algebras.Moreover,the cohomology theory of embedding tensors on 3-Hom-Lie algebras is defined.As an application,we show that if two linear deformations of an embedding tensor on a 3-Hom-Lie algebra are equivalent,then their infinitesimals belong to the same cohomology class in the first cohomology group.
基金Supported by the Fundamental Research Funds for the Central Universities
文摘Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F -algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to be an algebraically closed field of characteristic zero, K a finite group, F K the group algebra of K over F , then all local automorphisms of F K are also characterized.
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National Natural Science Foundation of China(12071405,11571145)。
文摘Some relationships between the representation of Hom-Jacobi-Jordan algebra and that of Jacobi-Jordan algebra are studied.Moreover,by using the notion ofαk-anti-derivation,a property theorem of multiplicative Hom-Jacobi-Jordan algebras is also given.
基金supported by the National Natural Science Foundation of China (Nos.12171290,12301152)the Natural Science Foundation of Shanxi Province (No.202203021222018)。
文摘In this paper,we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent,respectively,and then,as applications,we obtain the concrete characterizations of all nonadditive skew(anti-)commuting maps on some operator algebras.
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).
