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.

这个纯数学项目的重点是抽象代数和被称为算子代数的泛函分析领域之间的相互作用。具体来说，它的目的是处理一般化的图C*-代数和莱维特路代数。在过去的十年里，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，使他们能够系统地将技术和定理从一个转移到另一个。最近的研究表明，代数和C*-代数的广群模型可能提供了缺失的一环。这个项目旨在确定群胚在这两个理论中的作用，并分析和利用抽象代数和算子代数之间的协同作用。