Tau-倾斜模的相关问题研究
基本信息
结项摘要
Tau-tilting is a recent, important development in representation theory of algebras where tilting modules are replaced by so-called tau-tilting modules. In this project, we shall study tau-tilting modules in the context of 2-Calabi-Yau triangulated categories and higher cluster categories. Namely, we plan to study the relationship between tau-tilting modules and maximal rigid objects in 2-Calabi-Yau triangulated categories, to study the relationship between tau-tilting modules and d-cluster-tilting objects in higher cluster categories (d-cluster categories).
Tau-倾斜理论是代数表示论的最新进展之一，它是倾斜理论的重要延续。本项目拟在2-Calabi-Yau三角范畴和高维丛范畴的框架下研究tau-倾斜模的相关问题。具体研究，2-Calabi-Yau三角范畴里的极大rigid对象与相关自同态代数上的tau-倾斜模之间的关系；高维丛范畴里的d-cluster-倾斜对象与d-cluster-倾斜代数上的tau-倾斜模之间的关系。
项目摘要
本项目在2-Calabi-Yau三角范畴和高维丛范畴的框架下研究τ-倾斜模的相关问题。证明了2-Calabi-Yau三角范畴里的极大rigid对象与相应自同态代数上的支撑τ-倾斜对（support τ-tilting pairs）之间有一一对应的关系;证明了高维丛范畴里的部分高维丛倾斜对象压到高维丛倾斜代数上的τ-倾斜模，反过来，高维丛倾斜代数上的任意τ-倾斜模可以提升为高维丛范畴里的高维丛倾斜对象。
项目成果
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数据更新时间：2023-05-31
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