Classification of simple C*-algebras: inductive limits of matrix algebras over trees

In this book, it is shown that the simple unital $C^*$-algebras arising as inductive limits of sequences of finite direct sums of matrix algebras over $C(X_i)$, where $X_i$ are arbitrary variable trees, are classified by K-theoretical and tracial data.

This result generalizes the result of George Elliott of the case of $X_i = [0,1]$.

The added generality is useful in the classification of more general inductive limit $C^*$-algebras.