U.S.-Brazil Cooperative Science Program: Exchange Program in Representation Theory

这项美巴合作科学奖将支持弗吉尼亚理工学院和州立大学的Edward Green和巴西圣保罗大学的Eduardo Marcos的研究合作。本课题旨在通过研究两位研究者引入的局部理论，探索分级环的分级模的范畴。pi将调查两个具体问题。首先，他们将研究局部有限型的有限维代数（他们为分级代数定义了一个概念）。他们期望这些分级代数应该具有Auslander-Reiten颤振中“可分级”分量的数量是有限的性质。其次，他们将通过研究有限维代数上模范畴的等价子范畴来研究渐变局部交换代数上渐变Cohen-Macaulay模范畴的局部结构。美方将提供分级模块和有限维表示理论方面的专业知识。巴西方面将提供Cohen-Macaulay模块的专业知识。通过这次合作，双方将更好地理解表示理论，这是数学中的一个重要课题。

This US-Brazil Cooperative Science award will support the research collaboration of Edward Green of Virginia Polytechnic Institute and State University and Eduardo Marcos of the University of Sao Paulo, Brazil. The project aims to explore the category of graded modules of a graded ring by studying the local theory which the two researchers have introduced. The PIs will investigate two specific problems. First, they will study finite dimensional algebras which are locally of finite type (a notion they have defined for graded algebras). They expect that these graded algebras should have the property that the number of "gradable" components in the Auslander-Reiten quiver is finite. Second, they will investigate the local structure of the category of graded Cohen-Macaulay modules over a graded local commutative algebra by studying an equivalent subcategory of the category of modules over a finite dimensional algebra. The US side will contribute expertise in graded modules and finite dimensional representation theory. The Brazilian side will contribute expertise in Cohen-Macaulay modules. Through this collaboration, both sides will gain a better understanding of representation theory, an important topic in mathematics.