素的*-代数上的非线性混合Lie三重ξ-导子

THE MIXED LIE TRIPLE ξ-DERIVATION ON PRIME *-ALGEBRAS

本文刻画了素*代数上的非线性混合Lie三重ξ-导子(ξ≠1)的结构.利用皮尔斯分解和混合Lie三重ξ-导子的性质,证明了一个有单位元和非平凡投影的素*-代数上的非线性的混合Lie三重ξ-导子(ξ≠1)一定是可加导子,且关于ξ是线性的.

The aim of this paper is to characterize the nonlinear mixed Lie tripleξ-derivation(ξ=1)of a prime*-algebra.By using Peirce decomposition and the main proposition of mixed Lie tripleξ-derivation,it is proved that the nonlinear mixed Lie tripleξ-derivation(ξ=1)of a prime*-algebra with unit and non-trivial projection is an additive*-derivation and linear aboutξ.