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

这项美国-巴西合作科学奖将 支持爱德华的研究合作 弗吉尼亚理工学院的绿色和 州立大学和爱德华多·马科斯的 巴西圣保罗大学。 项目 旨在探讨分级模块的范畴 通过研究分次环的局部理论， 这是两位研究人员介绍的。 PI将调查两个具体问题。 首先，他们将研究有限维 局部有限型（a）代数 （他们为分次代数定义的概念）。 他们期望这些分次代数应该 具有“可分级”的数量 Auslander-Reiten曲线中的成分 有限的 其次，他们将调查 分次范畴的局部结构 分次局部上的Cohen-Macaulay模 通过研究等价的交换代数 模范畴的子范畴 有限维代数 美方将 在分级模块中贡献专业知识， 有限维表示理论 的 巴西方面将提供专业知识， Cohen-Macaulay模 通过这个 合作，双方将获得更好的 理解表征理论， 数学中的重要课题。

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.