By Lin H.
The speculation and purposes of C*-algebras are on the topic of fields starting from operator conception, workforce representations and quantum mechanics, to non-commutative geometry and dynamical structures. by means of Gelfand transformation, the idea of C*-algebras can be considered as non-commutative topology. a couple of decade in the past, George A. Elliott initiated this system of type of C*-algebras (up to isomorphism) through their K-theoretical info. It all started with the class of AT-algebras with genuine rank 0. considering the fact that then nice efforts were made to categorise amenable C*-algebras, a category of C*-algebras that arises so much obviously. for instance, a wide category of straightforward amenable C*-algebras is chanced on to be classifiable. the applying of those effects to dynamical platforms has been proven. This e-book introduces the new improvement of the speculation of the type of amenable C*-algebras - the 1st such try out. the 1st 3 chapters current the fundamentals of the idea of C*-algebras that are quite very important to the speculation of the class of amenable C*-algebras. bankruptcy four deals the type 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 direction on C*-algebras. The final chapters include extra complicated fabric. specifically, they take care of the category theorem for easy AH-algebras with actual rank 0, the paintings of Elliott and Gong. The e-book includes many new proofs and a few unique effects on the topic of the category of amenable C*-algebras. in addition to supplying an advent to the speculation of the class of amenable C*-algebras, it's a complete 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.