本项目主要研究Morita系统环上的保持映射问题，及其在算子理论中的应用，重点刻画Morita系统环上的李同构与李导子的形式和性质。我们已知三角代数和阶数大于2的全矩阵代数上的李同构俱有所谓的标准形式，因此猜想：Morita系统环上的李同构也俱有标准形式；这是本项目的核心研究目标。同时，我们将进一步刻画Morita系统环上的交换保持映射、李导子等与李理论紧密相连的映射的性质。最后，利用所获得的代数结论研究算子代数（包括套代数、von Neumann代数等）的性质以及Banach代数上算子的自动连续性。

In this project we main study the preserving mappings over the Morita context rings and their applications in operator theory. The main object is to characterize the Lie isomorphisms and Lie derivatiopns over the Morita context rings. We have known that the Lie isomorphisms of triangular algebras and full matrix algebras of order bigger than 2 are of the standard form. Hence we conjecture that the Lie isomorphisms of Morita context rings are also of the standard form and this is the core objective of this project. Moreover, we will study the properties of commutativity-preserving mappings, Lie derivations and some other mappings which are closely related to Lie theory. Finally, we will apply the algebraic results to operator algebras (including nest algebras, von Neumann algebras) and the theory of automatic continuity in Banach algebras.