This award supports cooperative research on linear algebra between Terry Loring of the University of New Mexico and Ruy Exel of the University of Sao Paulo in Brazil. Approximately finite-dimensional (AF) algebras are C*-algebras which are the inductive limits of algebras of matrices. Since the dimension of these matrices can grow arbitrarily fast in the inductive system, many of the results from linear algebra are not useful, at least in the context of AF algebras, because of the dependence on dimension. This research will attempt to develop new invariants of more general collections of matrices that almost satisfy a set of relations, especially invariants that will have an impact on research in C*-algebras. The most important rationale for this proposed collaboration is the complementary expertise of the applicants. The project will combine Exel's expertise in generalized determinants, and together with Loring's expertise in AF algebras and related issues in operator theory. Their combined expertise has led them to obtain some interesting invariants for the case of almost commuting matrices.
