Mathematical Sciences\RUI: Problems in Algebra: Group Actions on Trees and Buildings

数学科学RUI：代数问题：树木和建筑物的群作用

• 批准号: 9623282
• 负责人: Roger Alperin
• 金额: $ 3.61万
• 依托单位: San Jose State University Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-06-01 至 1998-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623282&HistoricalAwards=false
• 关键词: Mathematical; Sciences; RUI; Problems; Algebra

9623282 Alperin This grant supports the research of Professor R. Alperin to work on problems in the representation of finite groups on various geometric objects. In particular he wants to work on groups acting on trees, buildings and their generalizations. He hopes to use various fixed point properties as an aid in classifying certain groups with various homological or geometrical realizations. This is research in the field of group theory. Group theory can be thought of as the study of symmetry in the abstract. As such, this area has direct applications to many areas of physics and chemistry. Moreover, within the last 30 years, many connections to problems in data transmission have been solved using techniques from group theory. There are also direct connections to the error correcting codes that are vital for modern computing such as working with CD-ROM's.

9623282 Alperin这笔赠款支持R. Alperin教授的研究，以在各种几何对象的有限群体代表中处理问题。特别是他想在树木，建筑物及其概括上工作的团体工作。他希望使用各种固定点特性来帮助对某些具有各种同源或几何实现的群体进行分类。 这是小组理论领域的研究。可以将群体理论视为摘要中对称性的研究。因此，该领域直接应用于许多物理和化学领域。此外，在过去30年中，使用小组理论的技术解决了与数据传输问题的许多联系。与校正校正代码的直接连接对于现代计算至关重要，例如使用CD-ROM。