Totally disconnected groups and their algebras

完全不连通群和它们的代数。群是传递对称性的代数对象，就像\r\nnumbers传递大小一样。例如，一个\r\n晶体的对称性形成了一个晶体群，而\r\n晶体群的分类描述了所有可能的\r\n晶体结构。完全不连接的群产生于具有节点和“邻居”关系的网络结构的不对称，就像晶体模型一样，但不像晶体那样刚性。最近发现了用于分析完全\r\ndisconnected组的强大技术，而这个\r\nproject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理论的应用范围。\ r \ n

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