倾斜理论与例外序列

倾斜理论是有限维代数表示理论的核心理论，是近些年来同调代数等领域的研究热点之一。本项目致力于研究例外序列新的性质以及它们在Extriangulated范畴上与倾斜理论之间密切联系，具体如下：.1）探索例外模等相关倾斜对象在环扩张下的表现；.2）研究Extriangulated范畴上的例外序列，同时考虑Extriangulated范畴上的例外序列与现有的Extriangulated范畴上倾斜子范畴与Cluster-倾斜子范畴之间是否存在一一对应；.3）研究Extriangulated范畴上的τ-倾斜和Supportτ-倾斜理论，同时考虑Extriangulated范畴上的τ-例外序列与Extriangulated范畴上τ-倾斜和Supportτ-倾斜对象之间是否存在一一对应；.本项目的开展，将为倾斜理论的研究提供新的内容，进而为同调代数和代数表示理论的发展做出一定的贡献。

Tilting theory is a core theory of the representation theory of finite dimensional algebra, which is also a hot research topic in homological algebra and other fields. The present project is committed to studying some new propertites of exceptional sequences, and the close contact between tilting theory and exceptional sequences over extriangulated categories. The details are as follows:.1. Explore the expressions of tilting objects(especially, exceptional modules)over ring extensions..2. Study exceptional sequences over extriangulated categories, and whether the results have a one-to-one correspondence with the corresponding tilting subcategories or cluster-tilting subcategories over extriangulated categories..3. Investigate τ-tilting, support τ-tilting theory and τ-exceptional sequences over extriangulated categories, and whether the results have a one-to-one correspondence with each other..This project will provide a new content for the study of tilting theory, and then provide a certain contribution for the development of homological algebra and algebraic representation theory.