Groupoids as bridges between algebra and analysis

群形作为代数和分析之间的桥梁

• 批准号: DP150101598
• 负责人: Prof Aidan Sims
• 金额: $ 21.43万
• 依托单位: University of Wollongong
• 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: 2015-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP150101598
• 关键词: Groupoids; bridges; between; algebra; analysis

This pure mathematics project focuses on the interplay between abstract algebra and the area of functional analysis known as operator algebras. Specifically, it is intended to deal with generalisations of graph C*-algebras and of Leavitt path algebras. Over the last decade, researchers have discovered striking similarities between these areas, but no unifying result that would allow them to transfer techniques and theorems systematically from one to the other. Recent research suggests that groupoid models for both algebras and C*-algebras may provide the missing link. This project aims to determine the role of groupoids in the two theories, and analyse and exploit the resulting synergies between abstract algebra and operator algebras.

这个纯数学项目侧重于抽象代数和称为算子代数的泛函分析领域之间的相互作用。具体来说，它旨在处理图 C* 代数和 Leavitt 路径代数的推广。在过去的十年中，研究人员发现了这些领域之间惊人的相似之处，但没有统一的结果可以让他们系统地将技术和定理从一个领域转移到另一个领域。最近的研究表明，代数和 C* 代数的群群模型可能提供了缺失的环节。该项目旨在确定群形在这两种理论中的作用，并分析和利用抽象代数和算子代数之间产生的协同作用。