eb 2 00 9 CLASSIFICATION OF EXTENSIONS OF CLASSIFIABLE C ∗ - ALGEBRAS
نویسنده
چکیده
For a certain class of extensions e : 0 → B → E → A → 0 of C∗-algebras in which B and A belong to classifiable classes of C∗-algebras, we show that the functor which sends e to its associated six term exact sequence in K-theory and the positive cones of K0(B) and K0(A) is a classification functor. We give two independent applications addressing the classification of a class of C∗-algebras arising from substitutional shift spaces on one hand and of graph algebras on the other. The former application leads to the answer of a question of Carlsen and the first named author concerning the completeness of stabilized Matsumoto algebras as an invariant of flow equivalence. The latter leads to the first classification result for non-simple graph C∗-algebras.
منابع مشابه
2 7 Ju n 20 06 CLASSIFICATION OF EXTENSIONS OF CLASSIFIABLE C ∗ - ALGEBRAS
We classify extensions of certain classifiable C∗-algebras using the six term exact sequence in K-theory together with the positive cone of the K0-groups of the distinguished ideal and quotient. We then apply our results to a class of C∗-algebras arising from substitutional shift spaces.
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تاریخ انتشار 2009