Characterizations of Lie derivations of triangular algebras

Ji, Peisheng; Qi, Weiqing

doi:10.1016/j.laa.2011.02.048

Cited by 55 publications

(20 citation statements)

References 17 publications

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“…In this section, we give another characterization of ξ-Lie derivations on triangular algebras by acting on zero products. Since the cases ξ = 1 and ξ = 0 are considered in [10] and Theorem 3.1 respectively, we only deal with the case ξ = 0, 1. Our main result is the following.…”

Section: Elamentioning

confidence: 99%

Characterizing Lie derivations on triangular algebras by local actions

Qi¹

2013

ELA

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Abstract. Let U = Tri(A, M, B) be a triangular algebra, where A, B are unital algebras over a field F and M is a faithful (A, B)-bimodule. Assume that ξ ∈ F and L : U → U is a map. It is shown that, under some mild conditions, L is linear and satisfieswhere ϕ is a linear derivation, Z is a central element and f is a central valued linear map. For the case 1 = ξ ∈ F , L is additive and satisfies

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Section: Elamentioning

confidence: 99%

Characterizing Lie derivations on triangular algebras by local actions

Qi¹

2013

ELA

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“…AB = P). Later, this result was generalized to the maps on triangular algebras and prime rings in [10] and [20] respectively. Since factor von Neumann algebras are prime, Let A be an algebra over a field F. For a scalar ξ ∈ F and for A, B ∈ A, if AB = ξ BA, we say that A commutes with B up to a factor ξ .…”

Section: Introductionmentioning

confidence: 98%

Characterization of Lie derivations on von Neumann algebras

Hou

2013

Linear Algebra and its Applications

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Let M be any von Neumann algebra without central summands of type I 1 . For any scalar ξ , a characterization of any additive map Lis given: there exists an additive derivation ϕ such that, (1) if ξ = 1, then L = ϕ + f , where f is an additive map into the center vanishing on [A, B] with AB = 0; (2) if ξ = 0, then L(I) ∈ Z(M) and L(A) = ϕ(A) + L(I)A for all A; (3) if ξ is rational and ξ = 0, 1, then L = ϕ; (4) if ξ is not rational, then ϕ(ξ I) = ξ L(I) and L(A) = ϕ(A) + L(I)A.

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“…Let Clearly, each derivation is a Lie derivation. The Lie derivations on various kinds of rings and Algebras have been studied intensively (see [6,12,1,4,13,15,10,5]). Cheung in [6] described the form of Lie derivation on the triangular algebra.…”

Section: Introductionmentioning

confidence: 99%

Multiplicative Lie derivations on triangular n-matrix rings

Chen

2020

Linear and Multilinear Algebra

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A map φ on an associative ring is called a multiplicative Lie derivation if φ([x, y]) = [φ(x), y] + [x, φ(y)] holds for any elements x, y, where [x, y] = xy − yx is the Lie product. In the paper, we discuss the multiplicative Lie derivations on the triangular 3-matrix rings T = T3(Ri; Mij). Under the standard assumption QiZ(T )Qi = Z(QiT Qi), i = 1, 2, 3, we show that every multiplicative Lie derivation ϕ : T → T has the standard form ϕ = δ + γ with δ a derivation and γ a center valued map vanishing each commutator.2010 Mathematics Subject Classification. 16W25; 15A78; 47B47.

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Characterizations of Lie derivations of triangular algebras

Cited by 55 publications

References 17 publications

Characterizing Lie derivations on triangular algebras by local actions

Characterizing Lie derivations on triangular algebras by local actions

Characterization of Lie derivations on von Neumann algebras

Multiplicative Lie derivations on triangular n-matrix rings

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