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From the Basic Homotopy Lemma to the Classification of $C^*$-algebras

Huaxin Lin
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      This book examines some recent developments in the theory of $C^*$-algebras, which are algebras of operators on Hilbert spaces. An elementary introduction to the technical part of the theory is given via a basic homotopy lemma concerning a pair of almost commuting unitaries. The book presents an outline of the background as well as some recent results of the classification of simple amenable $C^*$-algebra, otherwise known as the Elliott program. This includes some stable uniqueness theorems and a revisiting of Bott maps via stable homotopy. Furthermore, $KK$-theory related rotation maps are introduced. The book is based on lecture notes from the CBMS lecture sequence at the University of Wyoming in the summer of 2015.
      Format: Paperback / softback CONTRIBUTORS: Huaxin Lin EAN: 9781470434908 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2017-11-01 CITY: GENRE: MATHEMATICS / Calculus WIDTH: 178 cm SPINE:

      Book Themes:

      Calculus

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      Huaxin Lin, East China Normal University, Shanghai, China, and University of Oregon, Eugene, OR.
      This book examines some recent developments in the theory of $C^*$-algebras, which are algebras of operators on Hilbert spaces. An elementary introduction to the technical part of the theory is given via a basic homotopy lemma concerning a pair of almost commuting unitaries. The book presents an outline of the background as well as some recent results of the classification of simple amenable $C^*$-algebra, otherwise known as the Elliott program. This includes some stable uniqueness theorems and a revisiting of Bott maps via stable homotopy. Furthermore, $KK$-theory related rotation maps are introduced. The book is based on lecture notes from the CBMS lecture sequence at the University of Wyoming in the summer of 2015.
      Format: Paperback / softback CONTRIBUTORS: Huaxin Lin EAN: 9781470434908 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2017-11-01 CITY: GENRE: MATHEMATICS / Calculus WIDTH: 178 cm SPINE:

      Book Themes:

      Calculus

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      Huaxin Lin, East China Normal University, Shanghai, China, and University of Oregon, Eugene, OR.

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