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

Hongbing Su

Jan 1995 · American Mathematical Society: Memoirs of the American Mathematical Society Book 547 · American Mathematical Soc.

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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.