An introduction to the classification of amenable by Lin H.

By Lin H.

The speculation and functions of C*-algebras are concerning fields starting from operator conception, team representations and quantum mechanics, to non-commutative geometry and dynamical platforms. by way of Gelfand transformation, the speculation of C*-algebras can be considered as non-commutative topology. a few decade in the past, George A. Elliott initiated this system of type of C*-algebras (up to isomorphism) via their K-theoretical info. It all started with the category of AT-algebras with actual rank 0. due to the fact that then nice efforts were made to categorise amenable C*-algebras, a category of C*-algebras that arises such a lot certainly. for instance, a wide type of easy amenable C*-algebras is came across to be classifiable. the applying of those effects to dynamical platforms has been proven. This e-book introduces the hot improvement of the speculation of the class of amenable C*-algebras - the 1st such try. the 1st 3 chapters current the fundamentals of the speculation of C*-algebras that are really vital to the idea of the category of amenable C*-algebras. bankruptcy four deals the type of the so-called AT-algebras of actual 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 complex fabric. particularly, they care for the class theorem for easy AH-algebras with genuine rank 0, the paintings of Elliott and Gong. The booklet includes many new proofs and a few unique effects relating to the class of amenable C*-algebras. in addition to offering an creation to the speculation of the class of amenable C*-algebras, it's a complete reference for these extra conversant in the topic.

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