Let A be a factor. For A, B ∈4, define by [A, B]. = AB- BA＊ the skew Lie product of A and B. In this article, it is proved that a map φ： A- A satisfies φ（[[A, B]., C].） = [[φ（A）, B]., C]. ＋ [[A, φ（B）]. C...Let A be a factor. For A, B ∈4, define by [A, B]. = AB- BA＊ the skew Lie product of A and B. In this article, it is proved that a map φ： A- A satisfies φ（[[A, B]., C].） = [[φ（A）, B]., C]. ＋ [[A, φ（B）]. C]. ＋ [[A, B]., φ（C）]. for all A, B, C∈ A if and only if φ is an additive ＊-derivation.展开更多
Let R be a 2-torsion free prime ring and L a noncommutative Lie ideal of R. Suppose that （d,σ） is a skew derivation of R such that xsd（x）xt = 0 for all x ∈ L, where s, t are fixed non-negative integers. Then d = 0.
Let T（n, R） be the Lie algebra consisting of all n× n upper triangular matrices over a commutative ring R with identity 1 and M be a 2-torsion free unital T（n, R）-bimodule. In this paper, we prove that every ...Let T（n, R） be the Lie algebra consisting of all n× n upper triangular matrices over a commutative ring R with identity 1 and M be a 2-torsion free unital T（n, R）-bimodule. In this paper, we prove that every Lie triple derivation d ： T（n, R） →M is the sum of a Jordan derivation and a central Lie triple derivation.展开更多
Let A be a von Neumann algebra with no central abelian projections. It is proved that if an additive map δ :A → A satisfies δ([[a, b], c]) = [[δ(a), b], c] + [[a, δ(b)], c] +[[a, b], δ(c)] for any a, b, c∈ A wi...Let A be a von Neumann algebra with no central abelian projections. It is proved that if an additive map δ :A → A satisfies δ([[a, b], c]) = [[δ(a), b], c] + [[a, δ(b)], c] +[[a, b], δ(c)] for any a, b, c∈ A with ab = 0(resp. ab = P, where P is a fixed nontrivial projection in A), then there exist an additive derivation d from A into itself and an additive map f :A → ZA vanishing at every second commutator [[a, b], c] with ab = 0(resp.ab = P) such that δ(a) = d(a) + f(a) for any a∈ A.展开更多
Let N be the Lie algebra of all n x n dominant block upper triangular matrices over a field F. In this paper, we explicitly describe all Lie triple derivations of N when char（F） ≠ 2. As an application, we character...Let N be the Lie algebra of all n x n dominant block upper triangular matrices over a field F. In this paper, we explicitly describe all Lie triple derivations of N when char（F） ≠ 2. As an application, we characterize Lie derivations of N when char（F） ≠ 2.展开更多
We study the Banach-Lie group Ltaut（A） of Lie triple automorphisms of a complex associative H^＊-algebra A. Some consequences about its Lie algebra, the algebra of Lie triple derivations of A, Ltder（A）, are obtain...We study the Banach-Lie group Ltaut（A） of Lie triple automorphisms of a complex associative H^＊-algebra A. Some consequences about its Lie algebra, the algebra of Lie triple derivations of A, Ltder（A）, are obtained. For a topologically simple A, in the infinite-dimensional case we have Ltaut（A）0 = Aut（A） implying Ltder（A） = Der（A）. In the finite-dimensional case Ltaut（A）0 is a direct product of Aut（A） and a certain subgroup of Lie derivations δ from A to its center, annihilating commutators.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11526123,11401273)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2015PA010)
文摘Let A be a factor. For A, B ∈4, define by [A, B]. = AB- BA＊ the skew Lie product of A and B. In this article, it is proved that a map φ： A- A satisfies φ（[[A, B]., C].） = [[φ（A）, B]., C]. ＋ [[A, φ（B）]. C]. ＋ [[A, B]., φ（C）]. for all A, B, C∈ A if and only if φ is an additive ＊-derivation.
基金The NSF(1408085QA08)of Anhui Provincialthe Key University Science Research Project(KJ2014A183)of Anhui Province of Chinathe Training Program(2014PY06)of Chuzhou University of China
文摘Let R be a 2-torsion free prime ring and L a noncommutative Lie ideal of R. Suppose that （d,σ） is a skew derivation of R such that xsd（x）xt = 0 for all x ∈ L, where s, t are fixed non-negative integers. Then d = 0.
基金Supported by the National Natural Science Foundation of China (Grant No. 10771027)
文摘Let T（n, R） be the Lie algebra consisting of all n× n upper triangular matrices over a commutative ring R with identity 1 and M be a 2-torsion free unital T（n, R）-bimodule. In this paper, we prove that every Lie triple derivation d ： T（n, R） →M is the sum of a Jordan derivation and a central Lie triple derivation.
基金supported by the National Natural Science Foundation of China(No.11401452)the China Postdoctoral Science Foundation(No.2015M581513)
文摘Let A be a von Neumann algebra with no central abelian projections. It is proved that if an additive map δ :A → A satisfies δ([[a, b], c]) = [[δ(a), b], c] + [[a, δ(b)], c] +[[a, b], δ(c)] for any a, b, c∈ A with ab = 0(resp. ab = P, where P is a fixed nontrivial projection in A), then there exist an additive derivation d from A into itself and an additive map f :A → ZA vanishing at every second commutator [[a, b], c] with ab = 0(resp.ab = P) such that δ(a) = d(a) + f(a) for any a∈ A.
文摘Let N be the Lie algebra of all n x n dominant block upper triangular matrices over a field F. In this paper, we explicitly describe all Lie triple derivations of N when char（F） ≠ 2. As an application, we characterize Lie derivations of N when char（F） ≠ 2.
基金Supported by the PCI of the UCA ‘Teoría de Lie y Teoría de Espacios de Banachthe PAI with project numbers FQM-298 and FQM-336the project of the Spanish Ministerio de Educación y Ciencia MTM2004-06580-C02-02 and with fondos FEDER
文摘We study the Banach-Lie group Ltaut（A） of Lie triple automorphisms of a complex associative H^＊-algebra A. Some consequences about its Lie algebra, the algebra of Lie triple derivations of A, Ltder（A）, are obtained. For a topologically simple A, in the infinite-dimensional case we have Ltaut（A）0 = Aut（A） implying Ltder（A） = Der（A）. In the finite-dimensional case Ltaut（A）0 is a direct product of Aut（A） and a certain subgroup of Lie derivations δ from A to its center, annihilating commutators.
