Mathematical Sciences: Graded AF Algebras and AF Algebra Bundles

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This is a research planning grant for the purpose of supporting Professor Parker's activities in a preliminary study of her proposed research project. The grant will provide funds for her to visit established research centers and consult with experts in the field. In addition she will attend several conferences and participate in research seminars. The project itself deals with C* algebras. 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 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 make them important to study.