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From the basic homotopy lemma to the classification of C*-algebras / Huaxin Lin.

By: Material type: TextTextSeries: CBMS-Regional conference series in mathematics ; no 124.Publication details: Providence : Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, ©2017.Description: vi, 240 pages ; 26 cmISBN:
  • 9781470434908 (alk. paper)
Subject(s): DDC classification:
  • 510 23 C748
Contents:
0. An overview of the Elliott program -- 1. An introduction to the Basic Homotopy Lemma -- 2. Maps to finite dimensional $C^*$-algebras -- 3. Stable homotopy lemmas -- 4. The Basic Homotopy Lemma, finite dimensional cases -- 5. $C^*$-algebras of generalized tracial rank one -- 6. More Basic Homotopy Lemmas -- 7. Asymptotic unitary equivalence -- 8. Classification of simple $C^*$-algebras of finite rank -- Bibliography -- Index.
Summary: 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.
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Includes bibliographical references and index.

0. An overview of the Elliott program --
1. An introduction to the Basic Homotopy Lemma --
2. Maps to finite dimensional $C^*$-algebras --
3. Stable homotopy lemmas --
4. The Basic Homotopy Lemma, finite dimensional cases --
5. $C^*$-algebras of generalized tracial rank one --
6. More Basic Homotopy Lemmas --
7. Asymptotic unitary equivalence --
8. Classification of simple $C^*$-algebras of finite rank --
Bibliography --
Index.

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.

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