Abstract
The extension of K-theory from topological spaces to operator algebras provides the most powerful tool for the study of C *-algebras. On one side there now exist far reaching classification results in which certain classes of C *-algebras can be classified by their K-theoretic data. This started with the early work of Elliott [Ell76] on the classification of AF-algebras – inductive limits of finite-dimensional C *-algebras. It went on with the classification of simple, separable, nuclear, purely infinite C *-algebras by Kirchberg and Phillips [KP00,Phi00]. Presently, due to the work of many authors (e.g., see [Win16] for a survey on the most recent developments) the classification program covers a very large class of nuclear algebras.
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Echterhoff, S. (2017). Bivariant KK-Theory and the Baum–Connes conjecure. In: K-Theory for Group C*-Algebras and Semigroup C*-Algebras. Oberwolfach Seminars, vol 47. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59915-1_3
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DOI: https://doi.org/10.1007/978-3-319-59915-1_3
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