非强极大的三角UHF代数上的Lie导子

Lie Derivations of Non-strongly Maximal Triangular UHF Algebras

讨论一类非强极大的三角UHF代数上的Lie导子.证明如果L是非强极大的三角UHF代数T上的Lie导子,则L形如D+λ,其中D是T上的结合导子,λ是从T到其中心Z上的线性映射且零化T中的括积.

This paper presents a study of Lie derivations of non-strongly maximal triangular UHF algebras. Results show that if L is a Lie derivation of a non-strongly maximal triangular UHF algebra T, then there exists an associative derivation D of T such that L = D ＋ λ, where λ is a linear map of T into its center which annihilates brackets of operators.