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这项拨款支持R. Alperin教授研究各种几何物体上有限群的表示问题。他特别想研究作用于树木、建筑物及其概括的群体。他希望利用各种不动点性质作为对具有各种同调或几何实现的特定群进行分类的辅助。这是群论领域的研究。群论可以被认为是对抽象对称性的研究。因此，这个领域对物理和化学的许多领域都有直接的应用。此外，在过去的30年里，许多与数据传输问题有关的问题已经用群论的技术解决了。还有与纠错码的直接联系，纠错码对现代计算至关重要，比如使用CD-ROM。