Operator algebras associated to semigroups and graphs

这个项目的目的是统一来自两个高度热门的数学领域的想法，在这两个领域中，一个人通过将离散对象表示为线性变换族来研究它们。在第一个区域中，一个表示将不可逆动力学建模为等距变换的半群；在第二个区域中，一个表示由部分定义的等距线族表示的网络，其方式反映了网络中路径的行为。这种联系将通过将它们生成的算子代数视为已被非对易上循环扭曲的半直积来实现。

This project aims to unify ideas from two highly topical areas of mathematics in which one studies discrete objects by representing them as families of linear transformations. In the first area, one represents the semigroups which model irreversible dynamics as isometries (that is, distance-preserving transformations); in the second, one represents networks by families of partially defined isometries in a way which reflects the behaviour of paths in the network. The link will be achieved by viewing the operator algebras they generate as semidirect products which have been twisted by a noncommutative cocycle.