By Lin H.
The speculation and functions of C*-algebras are on the topic of fields starting from operator idea, crew representations and quantum mechanics, to non-commutative geometry and dynamical structures. by way of Gelfand transformation, the speculation of C*-algebras can also be considered as non-commutative topology. a couple of decade in the past, George A. Elliott initiated this system of class of C*-algebras (up to isomorphism) by means of their K-theoretical info. It all started with the type of AT-algebras with actual rank 0. for the reason that then nice efforts were made to categorise amenable C*-algebras, a category of C*-algebras that arises so much clearly. for instance, a wide type of straightforward amenable C*-algebras is came across to be classifiable. the applying of those effects to dynamical structures has been verified. This booklet introduces the new improvement of the speculation of the category of amenable C*-algebras - the 1st such try. the 1st 3 chapters current the fundamentals of the idea of C*-algebras that are rather vital to the idea of the type of amenable C*-algebras. bankruptcy four deals the category of the so-called AT-algebras of genuine rank 0. the 1st 4 chapters are self-contained, and will function a textual content for a graduate path on C*-algebras. The final chapters comprise extra complicated fabric. specifically, they take care of the class theorem for easy AH-algebras with genuine rank 0, the paintings of Elliott and Gong. The e-book comprises many new proofs and a few unique effects concerning the category of amenable C*-algebras. in addition to supplying an creation to the speculation of the class of amenable C*-algebras, it's a finished reference for these extra accustomed to the topic.
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An introduction to the classification of amenable C-star-algebras by Lin H.