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An Introduction to C*-Algebras and Noncommutative Geometry
Buch von Heath Emerson
Sprache: Englisch

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Beschreibung
This is the first textbook on C*-algebra theory with a view toward Noncommutative Geometry. Moreover, it fills a gap in the literature, providing a clear and accessible account of the geometric picture of K-theory and its relation to the C*-algebraic picture. The text can be used as the basis for a graduate level or a capstone course with the goal being to bring a relative novice up to speed on the basic ideas while offering a glimpse at some of the more advanced topics of the subject. Coverage includes C*-algebra theory, K-theory, K-homology, Index theory and Connes¿ Noncommuntative Riemannian geometry.

Aimed at graduate level students, the book is also a valuable resource for mathematicians who wish to deepen their understanding of noncommutative geometry and algebraic K-theory. A wide range of important examples are introduced at the beginning of the book. There are lots of excellent exercises and any student working through these will benefit significantly. Prerequisites include a basic knowledge of algebra, analysis, and a bit of functional analysis. As the book progresses, a little more mathematical maturity is required as the text discusses smooth manifolds, some differential geometry and elliptic operator theory, and K-theory. The text is largely self-contained though occasionally the reader may opt to consult more specialized material to further deepen their understanding of certain details.
This is the first textbook on C*-algebra theory with a view toward Noncommutative Geometry. Moreover, it fills a gap in the literature, providing a clear and accessible account of the geometric picture of K-theory and its relation to the C*-algebraic picture. The text can be used as the basis for a graduate level or a capstone course with the goal being to bring a relative novice up to speed on the basic ideas while offering a glimpse at some of the more advanced topics of the subject. Coverage includes C*-algebra theory, K-theory, K-homology, Index theory and Connes¿ Noncommuntative Riemannian geometry.

Aimed at graduate level students, the book is also a valuable resource for mathematicians who wish to deepen their understanding of noncommutative geometry and algebraic K-theory. A wide range of important examples are introduced at the beginning of the book. There are lots of excellent exercises and any student working through these will benefit significantly. Prerequisites include a basic knowledge of algebra, analysis, and a bit of functional analysis. As the book progresses, a little more mathematical maturity is required as the text discusses smooth manifolds, some differential geometry and elliptic operator theory, and K-theory. The text is largely self-contained though occasionally the reader may opt to consult more specialized material to further deepen their understanding of certain details.
Über den Autor

Heath Emerson is Professor of Mathematics at the University of Victoria, British Columbia. His research interests include noncommutative geometry, equivariant K-theory, and the Baum-Connes conjecture.

Inhaltsverzeichnis

An introduction to C*-algebras.- An Introduction to Index Theory and Noncommutative Geometry.- Spectral Theory and Representation.- Positivity, Representations, Tensor Products and Ideals in C*-algebras.- Module theory of C*-algebras.- Morita Equivalence.- Topological K-theory and Clifford Algebras.- K-theory for C*algebras.- The Index Theorem of Atiyah and Singer.- K-homology and Noncommutative Geometry.- An Introduction to KK-theory.- Bibliography.

Details
Erscheinungsjahr: 2024
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Birkhäuser Advanced Texts Basler Lehrbücher
Inhalt: xiii
539 S.
27 s/w Illustr.
539 p. 27 illus.
ISBN-13: 9783031598494
ISBN-10: 3031598490
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Emerson, Heath
Hersteller: Springer International Publishing
Springer International Publishing AG
Birkhäuser Advanced Texts Basler Lehrbücher
Verantwortliche Person für die EU: Books on Demand GmbH, In de Tarpen 42, D-22848 Norderstedt, info@bod.de
Maße: 241 x 160 x 36 mm
Von/Mit: Heath Emerson
Erscheinungsdatum: 28.07.2024
Gewicht: 0,992 kg
Artikel-ID: 128860626
Über den Autor

Heath Emerson is Professor of Mathematics at the University of Victoria, British Columbia. His research interests include noncommutative geometry, equivariant K-theory, and the Baum-Connes conjecture.

Inhaltsverzeichnis

An introduction to C*-algebras.- An Introduction to Index Theory and Noncommutative Geometry.- Spectral Theory and Representation.- Positivity, Representations, Tensor Products and Ideals in C*-algebras.- Module theory of C*-algebras.- Morita Equivalence.- Topological K-theory and Clifford Algebras.- K-theory for C*algebras.- The Index Theorem of Atiyah and Singer.- K-homology and Noncommutative Geometry.- An Introduction to KK-theory.- Bibliography.

Details
Erscheinungsjahr: 2024
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Birkhäuser Advanced Texts Basler Lehrbücher
Inhalt: xiii
539 S.
27 s/w Illustr.
539 p. 27 illus.
ISBN-13: 9783031598494
ISBN-10: 3031598490
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Emerson, Heath
Hersteller: Springer International Publishing
Springer International Publishing AG
Birkhäuser Advanced Texts Basler Lehrbücher
Verantwortliche Person für die EU: Books on Demand GmbH, In de Tarpen 42, D-22848 Norderstedt, info@bod.de
Maße: 241 x 160 x 36 mm
Von/Mit: Heath Emerson
Erscheinungsdatum: 28.07.2024
Gewicht: 0,992 kg
Artikel-ID: 128860626
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