On the Classification of $C^*$-algebras of Real Rank Zero: Inductive Limits of Matrix Algebras over Non-Hausdorff Graphs

Download or read book On the Classification of $C^*$-algebras of Real Rank Zero: Inductive Limits of Matrix Algebras over Non-Hausdorff Graphs written by Hongbing Su and published by American Mathematical Soc.. This book was released on 1995 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work shows that $K$-theoretic data is a complete invariant for certain inductive limit $C^*$-algebras. $C^*$-algebras of this kind are useful in studying group actions. Su gives a $K$-theoretic classification of the real rank zero $C^*$-algebras that can be expressed as inductive limits of finite direct sums of matrix algebras over finite (possibly non-Hausdorff) graphs or Hausdorff one-dimensional spaces defined as inverse limits of finite graphs. In addition, Su establishes a characterization for an inductive limit of finite direct sums of matrix algebras over finite (possibly non-Hausdorff) graphs to be real rank zero.