POWRE: Problems in Noncommutative Algebra

在“非交换代数”项目期间，首席研究员将在加州大学圣地亚哥分校（1999年9月1日至12月24日）和加州伯克利数学科学研究所（2000年1月1日至6月30日）进行非交换代数的研究。这次研究休假将使她能够专注于她在非交换代数中存在的研究问题，目的是更好地理解非交换环的结构。她将继续研究非交换环的同调和维数理论问题（如Auslander-Gorenstein条件和滤波维数），上下代数的性质及其在微分偏序集表示理论中的应用，以及超代数的性质。研究休假还将为她提供非交换代数的新方法，特别是在非交换代数几何和组合代数技术方面；她还将学习更多关于量子群和相关环的应用。这十个月的研究休假将帮助她更好地研究非交换代数中的重要问题。该power项目由MPS多学科活动办公室（OMA）和数学科学部（DMS）联合支持。

The principal investigator will conduct research on noncommutative algebras at the University of California, San Diego (September 1 - December 24, 1999), and at the Mathematical Sciences Research Institute in Berkeley, California (January 1 - June 30, 2000), during the program on "Noncommutative Algebra." This research leave will enable her to focus on her existing research problems in noncommutative algebra, with the goal of providing a better understanding of the structure of noncommutative rings. She will continue her work on homological and dimension theoretic questions in noncommutative rings (e.g. the Auslander-Gorenstein condition and the filter dimension), on the properties of down-up algebras and theirapplication to the representation theory of differential partially ordered sets, and on properties of superalgebras. The research leave will also provide her with new methods in noncommutative algebra, particularly in noncommutative algebraic geometry and combinatorial algebraic techniques; she will also learn more about applications to quantum groups and related rings. The ten month research leave will help her become better able to pursue the important questions in noncommutative algebra. This POWRE project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).