On the Classification of C*-Algebras of Real Rank Zero: Inductive Limits of Matrix Algebras over Non-Hausdorff Graphs (Memoirs of the American Mathematical Society)

Su, Hongbing

ISBN 10: 0821826077 / ISBN 13: 9780821826072

Published by Amer Mathematical Society, 1995

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Bibliographic Details

• Title: On the Classification of C*-Algebras of Real Rank Zero: Inductive Limits of Matrix Algebras over Non-Hausdorff Graphs (Memoirs of the American Mathematical Society)
• Publisher: Amer Mathematical Society
• Publication Date: 1995
• Language: English
• ISBN 10: 0821826077
• ISBN 13: 9780821826072
• Binding: Paperback
• Condition: Fine

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Synopsis

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.