Scale-Multiplicative Semigroups and Geometry

尺度乘法半群和几何

• 批准号: DP150100060
• 负责人: Prof George Willis
• 金额: $ 30.62万
• 依托单位: The University of Newcastle
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2015
• 资助国家: 澳大利亚
• 起止时间: 2015-04-23 至 2019-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP150100060
• 关键词: Scale; Multiplicative; Semigroups; Geometry

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.

对称性在数学上是通过群的代数概念来处理的。相反，几何表示在群论中起着至关重要的作用。许多类的群，如物理学中出现的连通群，都有有用的几何表示，但在一般的不连通群的情况下，这种表示是缺乏的。某些不连通群，在代数上与连通群密切相关，确实有一种称为“建筑物”的几何表示。该项目旨在解决缺乏一般断开组的表示，通过扩展建筑物的概念来创建组合结构，这些组作为对称。