三角代数上Lie积为平方零元的非线性Jordan可导映射
Nonlinear Jordan derivable maps on triangular algebras by Lie product square zero elements

摘要： 设U=Tri(A, M, B )是特征不为 2 的三角代数, Q={u∈U:u2=0}且φ:U→U是一个映射(无可加或线性假设)。 证明了如果对任意a,b∈U且［a,b］∈Q, 有φ(ab)=φ(a)b+aφ(b), 则φ是一个可加导子, 其中［a,b］=ab-ba为Lie积, ab=ab+ba为Jordan积。
Abstract: Let U=Tri(A, M, B )be a 2-torsion free triangular algebra, and Q={u∈U:u2=0}. We prove that if a map φ:U→U satisfies φ(ab)=φ(a)b+aφ(b)for any a,b∈U with ［a,b］∈Q, then φ is an additive derivation, where ［a,b］=ab-ba is the Lie product and ab=ab+ba is the Jordan product