Mathematical Sciences: NSF/CBMS Regional Conferences in theMathematical Sciences; 'Hopf Algebras and Their Actions on Rings'; August 11-15, 1992

数学科学：NSF/CBMS 数学科学区域会议；

• 批准号: 9114403
• 负责人: Jeffrey Bergen
• 金额: $ 2.4万
• 依托单位: DePaul University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-11-15 至 1993-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9114403&HistoricalAwards=false
• 关键词: Mathematical; Sciences; NSF; CBMS; Regional

There has been renewed interest in Hopf algebras in the last several years because of the major example of quantum groups. General knowledge about Hopf algebras may be useful to those interested in quantum groups; conversely, quantum groups have introduced some new purely algebraic ideas into Hopf algebras. Independent of any connection to quantum groups, there have been many new developments in Hopf algebras, including the solution of two old conjectures. There has also been much work extending facts about group actions to actions and coactions of Hopf algebras. In addition, in light of the interest in Hopf algebra techniques in ring theory, operator algebras, and combinatorics, the field would appeal to an audience of Hopf algebraists, ring theorists, combinatorists, and operator algebraists. This project will support an NSF-CBMS Regional Research Conference in the Mathematical Sciences on Hopf Algebras and Their Actions on Rings to be held August 11-15, 1992 at DePaul University. Professor Susan Montgomery of the University of Southern California will be the principal lecturer. To stimulate interest and activity in mathematical research, the National Science Foundation each year supports a number of NSF-CBMS Regional Research Conferences in the Mathematical Sciences. Each five-day conference features a distinguished lecturer who delivers ten lectures on a topic of important current research in one sharply focused area of the mathematical sciences. The lecturer subsequently prepares an expository monograph based upon these lectures, which is normally published by the American Mathematical Society or the Society for Industrial and Applied Mathematics, or jointly by the American Statistical Association and the Institute of Mathematical Statistics. Certain features differentiate these conferences from typical research conferences. These are: (1) Focus on a single important and timely area of research by a leading practitioner, (2) Continued effect and local stimulation through regional emphasis, (3) Panel review for quality, breadth, and timeliness, and (4) Published monographs for a wider audience.

在过去的几年里，由于量子群的主要例子，人们对Hopf代数重新产生了兴趣。关于Hopf代数的一般知识可能对那些对量子群感兴趣的人有用；相反，量子群在Hopf代数中引入了一些新的纯代数思想。与量子群无关，Hopf代数有了许多新的发展，包括两个旧猜想的解决。也有很多工作将群作用的事实扩展到Hopf代数的作用和协同。此外，鉴于对Hopf代数技术在环理论、算子代数和组合中的兴趣，该领域将吸引Hopf代数学家、环理论家、组合学家和算子代数学家的听众。该项目将支持于1992年8月11-15日在DePaul大学举行的NSF-CBMS关于Hopf代数及其在环上的作用的数学科学区域研究会议。南加州大学的苏珊·蒙哥马利教授将担任首席讲师。为了激发人们对数学研究的兴趣和活动，美国国家科学基金会每年都支持一些NSF-CBMS数学科学区域研究会议。每个为期五天的会议都有一位杰出的讲师，他就一个重要的当前研究主题在数学科学的一个重点领域发表十次演讲。讲师随后根据这些讲座准备一篇说明性的专著，通常由美国数学学会或工业与应用数学学会出版，或由美国统计协会和数理统计研究所联合出版。这些会议的某些特点区别于典型的研究会议。这些是：(1)由一位领先的实践者专注于一个重要和及时的研究领域；(2)通过区域重点来持续影响和局部刺激；(3)对质量、广度和及时性进行小组审查；(4)为更广泛的受众出版专著。