Scale-Multiplicative Semigroups and Geometry

点击翻译按钮获取中文摘要

Symmetry is treated mathematically through the algebraic concept of a group. Conversely, geometric representations play a crucial role in group theory. Many classes of groups, such as the connected groups that arise in physics, have useful geometric representations, but such a representation is lacking in the case of general disconnected groups. Certain disconnected groups, closely related in algebraic terms to the connected ones, do have a geometric representation called a 'building'. This project aims to address the lack of a representation for general disconnected groups by extending the notion of a building to create combinatorial structures on which these groups act as symmetries.