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
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.
