Mathematical Sciences: Invariants of C*-Algebras

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DMS-9622434 Dadarlat Purdue University Research Fdn The investigator will continue his work on Elliott's program of classifying simple or real rank zero nuclear C*-algebras by K-theoretical and tracial invariants. This will involve research directed toward developing a local theory of approximately multiplicative completely positive maps of nuclear C*-algebras with algebraic invariants based on ordered mod-p K-theory. In a related direction the investigator will pursue the classification of simple or real rank zero subhomogeneous C*-algebras whose local spectra may have arbitrary dimension growth. He will study applications of the classification results into dynamics. C*-algebras can be thought as collections of infinite matrices of complex numbers displaying a rich algebraic structure. They correspond to a new idea of space: non-commutative or quantum space. Many singular spaces that are needed in the various areas of mathematics and physics can be successfully replaced by non-commutative C*-algebras. Remarkably, many of the tools of measure theory, topology, dynamics and differential geometry have powerful extensions to this non-commutative setting.