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

该奖项支持丹佛大学的Astrid和Huef博士、达特茅斯大学的Dana Williams博士和澳大利亚纽卡斯尔大学的Iain Raeburn博士在数学方面的一个为期三年的合作研究项目。这个项目将集中在三个目标上：1)证明非交换c代数上交换固有作用的对称非基性定理，2)证明这个新的对称非基性定理适用于各种各样的例子，3)将已知的关于简化交叉积的相关结果推广到完全交叉积。所提出的研究是算子代数理论的核心，在表示理论中具有应用价值。该项目汇集了三个具有互补专业知识和研究能力的实验室（两个在美国，一个在澳大利亚）的努力。Huef精通可积和固有作用的现代理论，Williams精通向量值积分和调和分析，Raeburn是非阿贝尔对偶的专家。这个项目将扩大我们的基础知识基础，促进国际间的了解与合作。

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.