三角代数上 Jordan 积为幂等元处的高阶ξ-Lie 可导映射
Higher ξ-Lie Derivable Maps on Triangular Algebras by Jordan Product Idempotents
设U=Tri(A,M,B)是三角代数,{φn}n∈N:U→U是一列线性映射.本文利用代数分解的方法,证明了如果对任意U,V∈U且U?V=P为标准幂等元,有φn([U,V]ξ=Σi+j=n(φi(U)φj(V)-ξφi(V)φj(U))(ξ≠1),则{φn}n∈N是一个高阶导子,其中φ0=id为恒等映射,U?V=UV+VU为Jordan积,[U,V]ξ=UV-ξVU为ξ-Lie积.
Let U=Tri(A, M, B) be a triangular algebra, and {φn}n∈N:U→U be a sequence of linear maps. In this paper, we prove that if {φn}n∈N satisfies φn([U, V]ξ)=Σi+j=n φi(U)φj(V)-ξφi(V)φj(U) for any U, V ∈ U with U?V=P being the standard idempotent, then {φn}n∈N is a higher derivation, where φ0=id is the identity map, U?V=UV+VU is the Jordan product and[U, V]ξ=UV-ξVU is the ξ-Lie product.
三角代数 / 高阶&xi / -Lie可导映射 / 高阶导子 {{custom_keyword}} /
triangular algebra / higher ξ-Lie derivable map / higher derivation {{custom_keyword}} /
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国家自然科学基金资助项目(11471199)
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