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

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。有关Hopf代数的一般知识对那些对量子群感兴趣的人可能是有用的；相反，量子群给Hopf代数引入了一些新的纯代数思想。与量子群无关，Hopf代数已经有了许多新的发展，包括解决了两个旧的猜想。也有许多工作将关于群作用的事实推广到Hopf代数的作用和余作用。此外，鉴于对Hopf代数技术在环论、算子代数和组合学中的兴趣，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。该项目将支持将于1992年8月11日至15日在德保罗大学举行的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力，美国国家科学基金会每年都会支持一些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发表十次演讲，该主题是数学科学中一个尖锐的重点领域。讲师随后根据这些讲座编写一份说明性专著，通常由美国数学学会或工业和应用数学学会出版，或由美国统计协会和数学统计研究所联合出版。这些会议的某些特点使其有别于典型的研究会议。它们是：(1)由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)小组审查质量、广度和及时性，以及(4)出版面向更广泛受众的专著。

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.