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

这项美国-巴西合作科学奖将支持弗吉尼亚理工学院和州立大学的爱德华·格林和巴西圣保罗大学的爱德华多·马科斯的研究合作。该项目旨在通过研究两位研究人员引入的局部理论来探索分次环的分次模范畴。警察督察将调查两个具体问题。首先，他们将研究局部有限类型的有限维代数(他们为分次代数定义的一个概念)。他们期望这些分次代数应该具有这样的性质，即Auslander-Reiten箭图中的“可分次”分支的数量是有限的。其次，他们将通过研究有限维代数上的模范畴的一个等价的子范畴来研究分次局部交换代数上的分次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。巴西方面将提供科恩-麦考利模块方面的专业知识。通过这次合作，双方将更好地理解数学中的一个重要课题--表示理论。

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.