Mathematical Sciences: Structure of semisimple Hopf algebras

数学科学：半简单 Hopf 代数的结构

• 批准号: 8701805
• 负责人: David Radford
• 金额: $ 4.88万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1990-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701805&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Structure; semisimple; Hopf

This research will investigate the structure of semisimple Hopf algebras, of Hopf algebra orders in group algebras, and of semisimple Hopf algebras which are semi-direct products. The research will focus on the structure of finite-dimensional semisimple Hopf algebras and the classification of such Hopf algebras in low dimension. In particular, a resolution of the Kaplansky conjecture will be sought. This research is in the general area of noncommutative ring theory. The research is concerned with the structure of Hopf algebras. An improved understanding of cosemisimple Hopf algebras could be of fundamental importance not just in Hopf algebra theory but in other fields as well. This an extremely difficult area but new techniques which have recently been introduced indicate that substantial progress can be expected.

本研究将研究半单的结构 Hopf代数，群代数中的Hopf代数阶， 半单Hopf代数是半直积。 的 研究将集中在有限维的结构 半单Hopf代数及其分类 低维代数 特别是， Kaplansky猜想将被寻求。 本文的研究是在非交换环的一般范畴内进行的 理论 本文研究的是Hopf的结构 代数 对余半单Hopf的进一步理解 代数不仅在Hopf中具有重要意义 代数理论，但在其他领域也是如此。 这是一个非常 困难的领域，但新的技术，最近已经 这表明可以预期取得实质性进展。