Locally compact groups and their C*-algebras

局部紧群及其 C* 代数

• 批准号: RGPIN-2018-05681
• 负责人: Wiersma, Matthew
• 金额: $ 1.68万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=713783
• 关键词: Locally; compact; groups; their; algebras

My research revloves around the intersection of two important areas of mathematics: groups and C*-algebras. Groups are one of the most fundamental structures in all of mathematics and originally arose by studying symmetries, whereas C*-algebras were developed early in the twentieth century in order to model phenomena occuring in quantum mechanics. My research focuses around a class of C*-algebras which arise from groups. To every locally compact group G, there are two natural constructions of C*-algebras: the full group C*-algebra C*(G) and the reduced group C*-algebra C*r(G). The class of group C*-algebras has been essential in developing a modern theory of C*-algebras and remains a very active area of research. Despite the importance of group C*-algebras, only the C*-algebras of discrete groups are well understood. This project seeks to better understand group C*-algebras of locally compact groups as a whole by investigating C*-algebras of classes of locally compact groups which "behave like" discrete groups.

我的研究涉及数学的两个重要领域：群和C*-代数。群是所有数学中最基本的结构之一，最初是通过研究对称性而产生的，而C*-代数是在世纪早期为了模拟量子力学中发生的现象而发展起来的。我的研究主要集中在一类C*-代数产生的群体。 对于每一个局部紧群G，有两种C*-代数的自然构造：全群C*-代数C*（G）和约化群C*-代数C*r（G）。群C*-代数类在发展现代C*-代数理论中是必不可少的，并且仍然是一个非常活跃的研究领域。尽管群C*-代数很重要，但只有离散群的C*-代数才被很好地理解。这个项目旨在通过研究“表现得像”离散群的局部紧群类的C*-代数来更好地理解局部紧群的群C*-代数。