Totally disconnected groups and their algebras

完全不连通的群及其代数。群是传达对称性的代数对象，就像数字传达大小一样。例如，一个晶体的对称性形成了一个晶体群，而晶体群的分类描述了所有可能的晶体结构。完全不连通的基团像晶体的模型一样，作为具有节点和\r\n关系的网络结构的对称性而产生，但不像晶体那样\r\n刚性。最近发现了用于分析完全\r\n不连通的群的强大技术，该项目旨在开发这些技术。由此产生的在理解对称性方面的重大进展将扩大群论的应用范围。\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