
From the Basic Homotopy Lemma to the Classification of $C^*$-algebras
Huaxin Lin(Author)
American Mathematical Society (Publisher)
Published on 30. October 2017
Book
Paperback/Softback
240 pages
978-1-4704-3490-8 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
Weight
440 gr
ISBN-13
978-1-4704-3490-8 (9781470434908)
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Schweitzer Classification
Person
Huaxin Lin, East China Normal University, Shanghai, China, and University of Oregon, Eugene, OR.
Content
An overview of the Elliott program
An introduction to the Basic Homotopy Lemma
Maps to finite dimensional $C^*$-algebras
Stable homotopy lemmas
The Basic Homotopy Lemma, finite dimensional cases
$C^*$-algebras of generalized tracial rank one
More Basic Homotopy Lemmas
Asymptotic unitary equivalence
Classification of simple $C^*$-algebras of finite rank
Bibliography
Index
An introduction to the Basic Homotopy Lemma
Maps to finite dimensional $C^*$-algebras
Stable homotopy lemmas
The Basic Homotopy Lemma, finite dimensional cases
$C^*$-algebras of generalized tracial rank one
More Basic Homotopy Lemmas
Asymptotic unitary equivalence
Classification of simple $C^*$-algebras of finite rank
Bibliography
Index