An Introduction to C*-Algebras and Noncommutative Geometry

• Verfasst von: Emerson, Heath [VerfasserIn]
• Titel: An Introduction to C*-Algebras and Noncommutative Geometry
• Verf.angabe: by Heath Emerson
• Ausgabe: 1st ed. 2024.
• Verlagsort: Cham
• Verlagsort: Cham
• Verlag: Springer International Publishing
• Verlag: Imprint: Birkhäuser
• E-Jahr: 2024
• Jahr: 2024.
• Jahr: 2024.
• Umfang: 1 Online-Ressource(XIII, 539 p. 27 illus.)
• Gesamttitel/Reihe: Birkhäuser Advanced Texts Basler Lehrbücher
• ISBN: 978-3-031-59850-0
• DOI: doi:10.1007/978-3-031-59850-0
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Emerson, Hearth: An introduction to C*-algebras and noncommutative geometry. - Cham, Switzerland : Birkhäuser, 2024. - xiii, 539 Seiten
• K10plus-PPN: 1896935850
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

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.

Abstract

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.