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

0124216an Huef 该奖项支持丹佛大学的 Astrid an 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 博士之间为期三年的数学合作研究项目。 该项目将重点关注三个目标：1) 证明用于在非交换 C 代数上交换适当动作的对称不等式定理，2) 证明这一新的对称不等式定理适用于各种示例，3) 将减少交叉积已知的相关结果扩展到完全交叉积。 所提出的研究是算子代数理论的核心，并应用于表示论。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，这三个实验室具有互补的专业知识和研究能力。 An Huef 精通可积和适当作用的现代理论，Williams 具有矢量值积分和调和分析方面的专业知识，Raeburn 是非阿贝尔对偶性方面的专家。 该项目将拓宽我们的基础知识基础，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.