Mathematical Sciences: Crossed Product Algebras and Non-Commutative Duality

点击翻译按钮获取中文摘要

Professor Gootman will continue his investigations concerning the ideal structure, representation theory, and dual topology of crossed product C*-algebras GxA determined by an action or coaction of a locally compact G on a C*-algebra A. As in the past, Professor Gootman will combine the three major methods for the study of such algebras: non-commutative duality theory, representation theory, and spectral methods (non-abelian harmonic analysis). Following such an approach, the proposer has already made progress on similar questions in collaboration with Professor Aldo Lazar. Professor Gootman will attempt to generalize a spectral characterization of simplicity of GxA which came out of this collaboration to general amenable G, and also to extend his investigations concerning the duality between induction and restriction of representations. This study should yield new information on ordinary crossed products, and in turn on groups, historically one of the major motivations for studying crossed products. The notion of a C* algebra is an abstraction of the idea of a family of linear transformations on a space. These transformations can also be thought of as having values in the states of the space, and the property of this family which is responsible for the symbol * is the fact that the algebra is generated by transformations whose values in these states are real numbers. The fact that these objects appear naturally in many branches of mathematics and physics makes them important to study.