关于算子代数上的线性映射的研究是算子代数领域的一个重要分支。导子、同态、Lie导子等线性映射在理论研究和实际应用中都有着重要的地位。Hilbert C*-模理论在算子代数理论中扮演着重要的角色，可以应用在很多方面，例如非交换几何、K-理论，以及椭圆算子的指标理论等等。因而 Hilbert C*-模算子代数是一类重要的算子代数。本项目拟考虑 Hilbert C*-模算子代数上的Lie导子及相关问题。

The study of linear mappings on operator algebras is an important branch of the field of operator algebra. Linear mappings, such as derivations, homomorphisms and Lie derivations, have an important position in both theoretical and practical applications. Hilbert C*- module theory plays an important role in the theory of operator algebras. It can be applied in many aspects, such as non-commutative geometry, K- theory, and index theory of elliptic operators. Therefore, the algebra of operators on Hilbert C*-modules is an important class of operator algebras. In this project, we consider Lie derivations and related problems on the algebra of operators on Hilbert C*-modules.