U.S.-Australia Cooperative Research: Proper Actions, Symmetric Imprimitivity Theorems, and Representations of Dynamical Systems

0124216 an Huef该奖项支持丹佛大学的Astrid an Huef博士、达特茅斯大学的Dana威廉姆斯博士和澳大利亚纽卡斯尔大学的Iain Raeburn博士之间为期三年的数学合作研究项目。 本项目将集中于三个目标：1）证明非交换C-代数上交换真作用的对称不变性定理，2）证明这个新的对称不变性定理适用于各种各样的例子，3）将约化交叉积的相关结果推广到全交叉积。 所提出的研究是中央在运营商代数理论和应用表示论。该项目汇集了三个实验室（两个在美国，一个在澳大利亚）的努力，这些实验室具有互补的专门知识和研究能力。 一个休夫是精通现代理论的可积和适当的行动，威廉姆斯的专业知识，在向量值的整合和谐波分析，和雷伯恩是专家nonabelian对偶。 该项目将扩大我们的基础知识，促进国际理解与合作。

0124216an HuefThis award supports a three-year collaborative research project in mathematics between Dr. Astrid an Huef of the University of Denver, Dr. Dana Williams of Dartmouth University, and Dr. Iain Raeburn of the University of Newcastle in Australia. This project will focus on three goals: 1) to prove a symmetric imprimitivity theorem for commuting proper actions on a non-commutative C-algebra, 2) to show that this new symmetric imprimitivity theorem applies in a wide variety of examples, and 3) to extend related results known for reduced crossed products to full crossed products. The proposed research is central in operator algebra theory and has applications to representation theory. The project brings together the efforts of three laboratories (two in the United States and one in Australia) that have complementary expertise and research capabilities. An Huef is well versed in the modern theory of integrable and proper actions, Williams has expertise in vector-valued integration and harmonic analysis, and Raeburn is an expert on nonabelian duality. This project will broaden our base of basic knowledge and promote international understanding and cooperation.