From the basic homotopy lemma to the classification of C*-algebras

Author(s)

• Lin, Huaxin
• Conference Board of the Mathematical Sciences

Bibliographic Information

From the basic homotopy lemma to the classification of C*-algebras

Huaxin Lin

（Regional conference series in mathematics, no. 124）

Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, c2017

• : pbk

Note

Published with support from the National Science Foundation

"NSF-CBMS Regional Conference in the Mathematical Sciences: the Basic Homotopy Lemma, the Asymptotic Uniqueness Theorem, and the Classification of C*-Algebras; held at the University of Wyoming, Laramie, WY, June 8-12, 2015."--T.p. verso

Includes bibliographical references (p. 233-238) and index

Description and Table of Contents

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.

Table of Contents

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

by "Nielsen BookData"

Details

• NCID: BB24300702
• ISBN:
  • 9781470434908
• LCCN: 2017014769
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Providence, R.I.
• Pages/Volumes: vi, 240 p.
• Size: 26 cm
• Classification:
  • LCC : QA612.7
  • DC23 : 515/.7
• Subject Headings:
  • LCSH : Homotopy theory
  • LCSH : Homotopy theory -- Problems, exercises, etc
  • LCSH : C*-algebras
  • LCSH : C*-algebras -- Problems, exercises, etc
• Parent Bibliography ID:
  • BA0000944X