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

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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.