Hecke Algebras in Algebra and Analysis

代数与分析中的赫克代数

• 批准号: LX0348081
• 负责人: Prof Iain Raeburn
• 金额: $ 3.53万
• 依托单位: University of Wollongong
• 依托单位国家: 澳大利亚
• 项目类别: Linkage - International
• 财政年份: 2003
• 资助国家: 澳大利亚
• 起止时间: 2003-01-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/LX0348081
• 关键词: Hecke; Algebras; Algebra; Analysis

The aim of this program is to adapt techniques from harmonic analysis and operator-algebraic representation theory to study Hecke algebras arising in algebraic and geometric settings. The relevant analytic structures are C*-algebras and the fundamental question is then "Which Hecke algebras have a faithful enveloping C*-algebra?" We investigate this question, first by developing an appropriate theory of crossed products by semigroups and, second, by using the notion of topologization which enables the Hecke algebra to be studied in the context of topological groups.

该计划的目的是适应技术从调和分析和运营商代数表示理论研究Hecke代数所产生的代数和几何设置。相关的解析结构是C*-代数，基本问题是“哪些Hecke代数有一个忠实的包络C*-代数？“我们研究这个问题，首先通过发展一个适当的理论交叉产品的半群，第二，通过使用的概念拓扑化，使赫克代数研究的背景下，拓扑群。