On the Structure of Lie Group C*-Algebras and Compact Quantum Groups

Abstract

We expose a K-theoretic approach to study group C*-algebras and C*-algebraic compact quantum groups: 1. The conception of multidimensional geometric quantization and the index of group C*-algebras; 2. the entire homology of noncommutative de Rham currents and the noncommutative Chern characters, and their computation for C*-algebras of compact Lie groups and compact quantum groups.