Totally disconnected groups and their algebras

完全不连通群及其代数

• 批准号: ARC : DP0208137
• 负责人: George Willis
• 金额: $ 18.5万
• 依托单位: The University of Newcastle
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2002
• 资助国家: 澳大利亚
• 起止时间: 2002-01-01 至 2005-12-31
• 项目状态: 已结题
• 来源: https://researchdata.edu.au/totally-disconnected-groups-algebras/75585
• 关键词: Totally; disconnected; groups; their; algebras

Totally disconnected groups and their algebras. Groups are algebraic objects which convey symmetry much as\r\nnumbers convey size. For example, the symmetries of a\r\ncrystal form a crystallographic group and the classification of\r\ncrystallographic groups describes all possible crystal\r\nstructures. Totally disconnected groups arise as\r\nsymmetries of network structures having nodes and a `neighbour'\r\nrelation, as models of crystals do, but which are not rigid like\r\ncrystals. Powerful techniques for analysing totally\r\ndisconnected groups have recently been discovered and this\r\nproject aims to develop those techniques. The resulting\r\nsignificant advances in the understanding of symmetry will\r\nextend the range of applications of\r\ngroup theory. \r\n

完全不连通群及其代数。群是代数对象，它们传递对称性，就像\r\n数字传递大小一样。例如，一个晶体的对称性形成一个晶体群，晶体群的分类描述了所有可能的晶体结构。完全不连通的群是作为具有节点和“邻居”关系的网络结构的对称性出现的，就像晶体模型一样，但它们不像晶体那样刚性。最近发现了用于分析完全不连通组的强大技术，本项目旨在开发这些技术。由此产生的对对称性理解的重大进展将扩展群论的应用范围。联系我们