环的优化扩张是同调代数中的重要研究对象, 并且与Frobenius扩张、cleft扩张以及正则扩张有密切关系。本项目将致力于研究优化扩张下Artin代数的一些表示不变量。以伴随对为工具，建立Artin代数的模范畴与其优化扩张的模范畴之间的联系。由此给出了倾斜代数以及A型和D型Dynkin图上遗传代数的优化扩张的刻画。与此同时，研究优化扩张下的Artin代数的表示维数。

Excellent extensions of rings are important research objects in homological algebra. Moreover, they are closely related with Frobenius extensions, cleft extensions and normalizing extensions. In this project, we will devote to studying several representation invariants of Artin algebras under excellent extensions. We will establish a relationship between module categories of an Artin algebra and its excellent extension by means of an adjoint pair. From this, we will give characterizations of excellent extensions of tilted algebras and the finite dimensional hereditary algebras of Dynkin diagrams A and D. Meanwhile the representation dimensions of Artin algebras under excellent extensions are also studied.