三角代数上Lie三重导子的刻画
Characterizations of Lie Triple Derivations on Triangular Algebras
设U=Tri(A,M,B)是三角代数.证明了在一般的假设下,如果线性映射δ:U→U,满足对任意的U,V,W∈U且UV=UW=0(或UV=UW=0),有δ([[U,V],W])=[[δ(U),V],W]+[[U,δ(V)],W]+[[U,V],δ(W)],则对任意U∈U,δ(U)=φ(U)+h(U),其中φ:U→U是一个导子,线性映射h:U→Z(U),满足对任意的U,V,W∈U且UV=UW=0(或UV=UW=0),有h([[U,V],W])=0.
Let U=Tri(A, M, B) be a triangular algebra.In this paper, under mild assumptions, we prove that if δ:U→U is a linear map satisfying δ([[U, V], W])=[[δ(U), V], W]+[[U, δ(V)], W]+[[U, V], δ(W)], for any U, V, W∈U with UV=UW=0(resp.UV=UW=0), then δ(U)=Φ(U)+h(U) for any U∈U, where Φ:U→U is a derivation, h:U→Z(U) is a linear map vanishing at second commutators with UV=UW=0(resp.UV=UW=0).
三角代数 / Lie三重导子 / Jordan积 {{custom_keyword}} /
triangular algebra / Lie triple derivation / Jordan product {{custom_keyword}} /
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国家自然科学基金资助项目(11471199)
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