Morita代数的表示和同调理论

本项目研究双中心化子性质与单态射范畴的联系，以及后者的导出范畴位于ladder中的条件；研究Morita代数的导出范畴与其Gorenstein投射模的稳定范畴位于ladder中的条件；研究Morita代数的导出单性。.. 我们将利用态射范畴等价的多次转化，研究双中心化子性质。通过单态射范畴到Morita环模范畴的嵌入，以ladder为工具，研究Morita代数与相关单态射范畴的导出范畴，以及Morita代数上Gorenstein投射模的稳定范畴，期望判定Morita代数的导出单性，在相关领域取得创新性成果。.. 本项目对进一步揭示 Gorenstein同调代数、表示论和三角范畴之间的联系，具有重要的科学意义和应用价值。

This project studies relations between double centralizer properties and the related monomorphism categories, and conditions when the derived categories of the latter sit in a ladder. We will study conditions when the derived categories and the stable categories of Gorenstein projective modules of the related Morita algebras sit in a ladder. We will characterize the derived simpleness of Morita algebras. .. By using several equivalences between the involved morphism categories, we will characterize the double centralizer properties. Via the embeddings of the related monomorphism categories into the module categories of some Morita rings, and using ladders, we will study the derived categories of Morita algebras and the related monomorphism categories, and the stable categories of their Gorenstein projective modules. We expect to give a criterion for the derived simpleness of Morita algebras. We hope to obtain a series of new results in the related fields. .. This project will further explore relations among Gorenstein homological algebra, representation theory of Artin algebras, and the theory of triangulated categories. It will be of significance in mathematics and of value in applications.