Operator algebras associated to semigroups and graphs

该项目旨在统一两个高度热门的数学领域的思想，其中一个研究离散对象，将它们表示为线性变换的家族。在第一个区域，将不可逆动力学模型表示为等距（即保持距离的变换）的半群；在第二种方法中，用部分定义的等距图族来表示网络，这种方式反映了网络中路径的行为。通过将它们生成的算子代数看作是被非交换环扭曲的半直积来实现这种联系。

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.