Morita 型稳定等价是代数表示论中的重要研究课题，它与 Hochschild (上)同调理论有密切的联系。本项目研究 Morita 型稳定等价的 Auslander-Reiten 猜想与 Hochschild 上同调代数的结构。具体地，我们将考虑具有多项式增长表示型的代数的 Auslander-Reiten 猜想；计算单项式代数以及 Koszul 代数等若干重要代数类的Hochschild上同调代数的Gertanhebaer李代数结构；考察 Hochschild 上同调代数结构与其箭图的组合性质的关系。本项目的研究将推进 Auslander-Reiten 猜想的研究，有助于理解 Hochschild 上同调与代数形变理论以及箭图组合之间的关系。

The study of stable equivalences of Morita type is an important research subject in representation theory of algebras, and it has closed relation with Hochschild (co)homology theory. This project studies the Auslander-Reiten conjecture for stable equivalences of Morita type and Hochschild cohomology rings of algebras. More precisely, we will investigate the Auslander-Reiten conjecture for algebras of polynomial growth; we will also compute the Gerstenhaber Lie algebra structure over the Hochschild cohomology rings of several important classes of algebras, such as monomial algebras and Koszul algebras; we will study the relation between Hochschild cohomology algebras and quiver combinatorics. The study we carry out in this project will contribute to our understanding of the Auslander-Reiten conjecture, and it will help us to understand the relation between Hochschild cohomology, algebraic deformation theory and quiver combinatoics.